padrões geográficos e temporais na riqueza de espécies de ... · eu gostaria de agradecerao dr....
TRANSCRIPT
Universidade Federal de Goiás
Instituto de Ciências Biológicas
Programa de Pós-Graduação em Ecologia e Evolução
Padrões geográficos e temporais na riqueza de espécies de
Quirópteros: mecanismos ecológico-evolutivos e incertezas
Discente: Davi Mello Cunha Crescente Alves
Orientador: José Alexandre Felizola Diniz-Filho
Co-Orientador: Fabricio Villalobos
Goiânia
20/03/2017
Eu gostaria de dedicar essa tese
ao meu padrinho Rodrigo, aquele que sempre esteve lá.
Agradecimentos
Agradecer não é uma tarefa fácil, mas é uma tarefa essencial para qualquer trabalho
realizado. Porque até aonde sei, nenhum trabalho é realizado sozinho. Por isso, eu
gostaria de começar agradecendo toda a minha família que esteve comigo desde o
começo, principalmente a minha avó "mãe" Maria Helena, meu avô "pai" Valter, minha
irmã Luna e o meu sobrinho e sobrinhas, minha mãe Patrícia, meu pai Sérgio, minha
madrasta Cláudia, minha irmãzinha Maria Rita, meus tios e tias maternos e paternos,
principalmente o meu padrinho Rodrigo. Sem vocês eu não teria "dado conta"!
Eu gostaria de agradecer a todos os meus amigos e amigas que são de "fora" da
Universidade, principalmente o Carlos Alberto "Guaraná", Giovani "Jagunço", Murilo,
Evaristo e Zanzaque convivem comigo semanalmente a vários e vários anos. Agradecer a
todos os meus amigos e amigas que são de "dentro" da Universidade. Principalmente ao
Lucas, Luciano, Jesús, Danilo, Kléber, Júlio, Fabricio e Lorena. Sem vocês não teria graça!
Eu gostaria de agradecerao dr. Daniel Brito, por ter me aceitado como seu orientando na
mestrado depois de muitos "nãos" e me aconselhadoposteriormente a buscarnovos
horizontes (mesmo que seja no laboratório ao lado!). Muito obrigado ao Dr. José
Alexandre Felizola Diniz-Filho por ter me acolhido no doutorado e ser "o" exemplo do que
é ser um bom profissional. Não se trata apenas do compromisso com o ofício mas
também do "trato" com as pessoas! E também muito obrigado ao Dr. Fabricio Villalobos
por toda a ajuda no doutorado (e também no mestrado!). Muito obrigado por todas as
"broncas", todos os "toques" e toda atenção. Você foi a pessoa que mais me ajudou no
doutorado! Sem vocês eu não saberia o caminho!
Muito obrigado a todos os professores, técnico-administrativos e terceirizados da
Universidade Federal de Goiás. Muito obrigado a todos os cientistas que eu tive a
oportunidade de ler suas obras. E por fim, muito obrigado ao povo brasileiro que me
pagou pra "estudar" mesmo com muito de seus filhos passando fome!
Sumário:
Resumo Geral ..................................................................................................................pg. 5
Apresentação ..................................................................................................................pg. 7
Capítulo 1 ......................................................................................................................pg. 13
Capítulo 2.1 .............................................................................................................. .....pg. 40
Capítulo 2.2 ................................................................................................................ ...pg. 77
Capítulo 3 ......................................................................................................................pg. 88
Capítulo 4 ................................................................................................ ....................pg. 125
Conclusão Geral ...........................................................................................................pg. 148
Apêndice 1 ...................................................................................................................pg. 149
Apêndice 2.1 ................................................................................................................pg. 151
Apêndice 2.2 ................................................................................................................pg. 169
Apêndice 3 ...................................................................................................................pg. 178
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Resumo Geral
Nessa tese nós tentamos entender quais são os fatores ecológicos e evolutivos
responsáveis por explicar a variação na riqueza de espécies de morcegos tanto entre
regiões quanto ao longo do tempo profundo. No primeiro capítulo nós avaliamos como
diferentes propriedades do ambiente - i.e. energia, heterogeneidade ambiental e
sazonalidade - explicam a riqueza de espécies de morcegos em diferentes regiões da
Terra. Nós encontramos que as contribuições contribuições por esses determinantes
ambientais para explicar os gradientes geográficos de morcegos são mais importantes do
que as suas contribuições específicas. Com o objetivo de entender mais especificamente
como processos históricos explicam a diferença de riqueza de morcegos entre regiões, nós
avaliamos no segundo capítulo a diferença de diversificação e dispersão biogeográfica
entre regiões tropicais e extratropicais. Além disso, nós avaliamos como a incerteza nos
dados e erros estatísticos associados aos modelos evolutivos que estimam esses processos
históricos podem afetar as nossas conclusões sobre o padrão geográfico dos morcegos.
Nós concluímos que esse padrão é extremamente afetado por esses dois artefatos. No
terceiro capítulo nós exploramos como o nosso conhecimento sobre as taxas de
diversificação estimadas por esses modelos evolutivos pode ser aprofundado se nós
levarmos em consideração a hierarquia biológica. Mais precisamente, nós propomos um
modelo conceitual para discutir se os padrões de diversificação são mais determinados
por processos evolutivos ocorrendo ao nível dos indivíduos que compõem as espécies ou
ao nível das próprias espécies. Já no último capítulo, nós avaliamos quais são os principais
fatores responsáveis por explicar a variação na riqueza de espécies de morcegos ao longo
do tempo profundo. Nós encontramos que a competição entre linhagens de morcegos por
nichos vagos ao longo do Cenozóico foi mais importante do que o efeito direto de
processos ambientais ocorrendo em grandes escalas geográficas, como mudanças
climáticas ou soerguimento de cadeias de montanhas. Finalizando, nós concluímos que
entre diferentes regiões, a sinergia entre processos ambientais é mais importante em
explicar a riqueza de espécies de morcegos do que o efeito específico de cada um. Já, ao
longo do tempo profundo, a competição por nichos vagos entre linhagens do mesmo
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clado é mais importante que o efeito direto de diferentes processos ambientais. Além
disso, nós também encontramos que problemas associados aos dados e modelos
evolutivos, assim como a falta de conhecimento dos mecanismos ecológico-evolutivos
subjacentes as esses modelos, podem afetar drasticamente as nossas conclusões a
respeito dos padrões de riqueza de espécies.
7
Apresentação
De antemão, eu gostaria de esclarecer que eu optei por fazer uma Apresentação da tese
mais informal, muito parecida com um prefácio de um livro. Portanto, me desculpem a
falta de um rigor característico de textos científicos, como objetividade na escrita ou
presença de citações da literatura científica. Eu optei por uma escrita que me desse mais
liberdade de expressar as idéias que nortearam a minha cabeça ao longo desses quatro
anos de doutorado e também que representasse uma conversa com algum familiar ou
pessoa de uma área do conhecimento diferente da Biologia. De qualquer forma, essa
informalidade é restrita à Apresentação, enquanto os capítulos são escritos de acordo
com as regras gerais de uma redação mais científica.
Eu gostaria de começar pensando sobre quais são os fatores que afetam a
biodiversidade. Entretanto, antes de entender o quê afeta a biodiversidade, é necessário
primeiramente pensar sobre como a biodiversidade se mostra aos nossos olhos. Nós
podemos pensar a biodiversidade como a quantidade de plantasque se encontram num
parque da nossa cidade, ou na quantidade de plantas que se encontram na Amazônia.
Essas foram as duas primeiras formas de pensar a biodiversidade que vieram na minha
cabeça e que talvez sejam próximas de exemplos que poderiam ser dados por qualquer
pessoa. É interessante pensar que ambos os exemplos possuem um
importantecomponente em comum: ageografia. Eles falam sobre a quantidade de plantas
que se encontram em um pequeno parque ou na grande floresta Amazônica. Nesse
sentido, se o nosso objetivo é compreender os fatores que regulam a biodiversidade, esse
recorte geográfico é extremamente importante. Será que os fatores que afetam a
quantidade de plantas no parque são os mesmos fatores que afetam a quantidade de
plantas na Amazônia? Essa pergunta se baseia na ideia de que a escala geográfica em que
esses fatores se encontram podem interferir no efeito que esses fatores possuem sobre a
biodiversidade.E essa escala é um componente que está diretamente ligado com a
capacidade das pessoas, mesmo que de forma inconsciente, de formularem hipóteses
plausíveis para entender a biodiversidade. Por exemplo, a grande maioria das pessoas,
quando indagadas sobre quais são os fatores que determinam a diferença na riqueza de
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espécies de plantas entre um parque no centro da cidade e outro parque mais na
periferia, provavelmente não irão saber responder rapidamente. Entretanto, se essas
mesmas pessoas forem indagadas sobre quais fatores que explicam a diferença na riqueza
de espécies entre a Amazônia e o Cerrado, elas rapidamente responderão que é o clima.
O clima, como um processo ambiental estruturante de biodiversidade em grandes
escalas geográficas, "ronda a cabeça" dos cientistas europeus a séculos. Desde o século
XVIII, cientistas como Alexander Von Humboldt e Alfred Wallace discutem como
gradientes geográficos de riqueza de espécies são afetados de diferentes formas pelo
clima. Entretanto, esses autores possuíam poucos dados empíricos para entender como
processos ambientais ocorrendo em grandes escalas geográfica poderiam afetar a
biodiversidade e, por conta disso, muito dessa linha de pesquisa se restringiu até pouco
tempo atrás apenas à elaboração de hipóteses científicas. Apenas com a grande
disponibilidade de variáveis climáticasao longo do globo, assim como o conhecimento
sobre a distribuição geográfica para várias espécies, é que essas teorias envolvendo o
clima puderam ser testadas formalmente. Os resultados, em sua grande maioria,
confirmaram as expectativas iniciais dos processos climáticos como um dos principais
fatores para explicar os gradientes geográficos de riqueza de espécies.
Nesse sentido, a grande maioria das pessoas leigas em Ecologia e Evolução estão,
pelo menos parcialmente, corretas: o clima é responsável em determinar os gradientes
geográficos de riqueza de espécies. Mas, então, será que a "grande" pergunta já foi
respondida ou será que o "buraco é mais embaixo”? É a partir desse momento que
perguntas mais complexas e interessantes sobre biodiversidade começam a surgir. Será
que outros processos ambientais, como topografia e biomassa vegetal, também são
importantes? Será que o ambiente afeta a biodiversidade da mesma forma em toda
regiões da Terra? Será que é o ambiente atual ou o ambiente do passado que foi mais
importante para estruturar geograficamente a riqueza de espécies?
Além dessas perguntas para entender a biodiversidade ao longo do espaço
geográfico, outra questão bastante interessante é entender como a biodiversidade varia
9
ao longo do tempo profundo. Quando nós pensamos em variação da biodiversidade em
grandes escalas temporais, por exemplo, durante os últimos 60 milhões de anos, é preciso
pensar automaticamente nos processos que são os responsáveis direto pela quantidade
de espécies na Terra. Esses processos evolutivos são: i) especiação, que é a quantidade de
espécies que surgem, ii) extinção, que é a quantidade de espécies que desaparecem, e iii)
diversificação, que é o balanço entre esses dois processos evolutivos. A partir daí, outras
perguntas sobre biodiversidade surgem, por exemplo: Como esses processos evolutivos
variam entre diferentes regiões da Terra? Como esses processos evolutivos variam
durante os períodos geológicos? Ou como o ambiente se associa com esses processos
evolutivos para determinar dinâmicas de biodiversidade ao longo do tempo profundo?
Essas perguntas levantadas acima, de longe, não são as únicas que permeiam a
explicação sobre a origem e manutenção da biodiversidade. Massão as mais interessantes
e as que "rondaram a minha cabeça" ao longo desses últimos quatro anos. Nesse sentido,
eu tentei, de alguma forma, responder nos quatro capítulos que fazem parte dessa tese
quais são os fatores mais importantes para explicar a variação da biodiversidade ao longo
do espaço geográfico e do tempo. Como os capítulos estão escritos em forma de artigo e,
portanto, não estão diretamente relacionados entre si, eu irei resumir mais adiante cada
um dos capítulos e mostrar como eles se relacionam para tentar responder a pergunta
central que norteiou esse trabalho. Mas, antes, eu irei falar brevemente sobre o grupo de
organismo que foi utilizado por mim e pelos co-autores para representar a diversidade
biológica da Terra.
Sobre a escolha dos organismos
Para entender a biodiversidade, nós precisamos ter toda informação sobre ela,
certo? Não necessariamente. Nós podemos tirar conclusões sobre o "todo" a partir de
uma "parte". Assim, nós podemos concluir sobre a biodiversidade a partir de um grupo
que represente a biodiversidade. Pensando nisso, faria sentido escolher um grupo que
conseguisse representar ao máximo essa biodiversidade, e para isso seria
necessário:apresentar uma grande variedade de formas de vida; se distribuir ao longo de
10
várias regiões e também ter passado por alguns dos grandes eventos ambientais que a
Terra sofreu; além disso, que possua dados disponíveis para documentar todas essas
informações. Os morcegos são um grupo que possui todas essas características!
Resumo dos capítulos
No primeiro capítulo nós tentamos responder se o ambiente afeta a riqueza de
morcegos da mesma forma em todas as regiões do mundo. Para isso, nós utilizamos um
modelo espacial não-estacionário para decompor a contribuição de diferentes processos
ambientais - como energia, heterogeneidade ambiental e sazonalidade - para o gradiente
de riqueza de morcegos em diferentes regiões da Terra. Nós mostramos que o ambiente
afeta a riqueza de morcegos diferentemente ao longo do globo e que a contribuição
compartilhada entre esses processos é bem mais importante do que a contribuição
específica de cada um.
No segundo capítulo, nós exploraramos diretamente como processos
macroevolutivos - como especiação, extinção e dispersão biogeográfica - são responsáveis
pela diferença na riqueza de espécies de morcegos entre regiões tropicais e extratropicais.
Para isso, nós utilizamos um método filogenético comparativo para estimar a
diversificação e dispersão de morcegos associadas às regiões geográficas mencionadas
acima. Entretanto, nós decidimos mudar o foco no decorrer das análises e testar como
incertezas associadas aos dados geográfico e filogenéticos, assim como taxas de Erro Tipo
I do método, poderiam "mascarar" as nossas explicações para o padrão global de riqueza
de morcegos. Além disso, nós realizamos um segundo capítulo (2.2), em que nós
avaliamos as taxas de Erro Tipo I de um modelo de diversificação dependente da geografia
bastante parecido com o do trabalho anterior mas para avaliar a riqueza global de
espécies de aves. Esse trabalho é na verdade uma re-análise de um trabalho publicado a
pouco tempo. No final, encontramos que tanto a incerteza nos dados, quanto as altas
taxas de Erro Tipo I de ambos os modelos, afetam bastante as nossas explicações para os
gradientes geográficos de riqueza de espécies de morcegos e aves.
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Já o terceiro capítulo surgiu da idéia de tentar compreender mais
"mecanisticamente"como funcionam esses modelos que estimam diversificação. Os
modelos do segundo capítulo fazem parte de um conjunto de modelos filogenéticos que
assumem que os atributos das linhagens - como tamanho corporal, nicho ecológico ou, no
nosso caso, as regiões em que as espécies atuais ocorrem - são responsáveis por
determinar as taxas de diversificação do clado. Portanto, esses modelos assumem
indiretamente que a interação entre os atributos das linhagens com o ambiente em que
essas linhagens se estabeleceram ao longo do tempo são responsáveis por um sucesso
evolutivo diferencial entre as mesmas. Como nós estamos pensando a nível de linhagens,
sucesso evolutivo se traduz em altas taxas de diversificação, o que seria análogo a pensar
em altas taxas reprodutivas a nível de indivíduos. Essa é a idéia do mecanismo de Seleção
Natural atuando ao nível de espécies e não ao nível de indivíduo como propõe a teoria
darwiniana clássica. Uma pergunta interessante que surge desse debate é sobre o que
mais afeta as taxas de diversificação de um clado: os atributos dos indivíduos que compõe
as espécies ou o próprio atributo das espécies? Nesse sentido, nós formulamos um
modelo conceitual que propõe premissas e predições para testar se as taxas de
diversificação dos clados são mais afetadas pelo processo seletivo atuando sobreos
atributos dos indivíduos que compõe as espécies ou pelos próprios atributos das espécies.
No último capítulo, nós tentamos compreender quais são os principais fatores para
determinar a dinâmica de riqueza de espécies de morcegos ao longo do tempo profundo.
As duas principais explicações para esse padrão de biodiversidade é o efeito direto de
processos ambientais em grandes escalas - como mudanças climáticas, variações no nível
do mar ou soerguimento de cadeias de montanhas - ou o efeito indireto desses processos
mediando a competição de linhagens por nichos vagos ao longo do tempo. Para isso, nós
utilizamos métodos filogenéticos comparativos que estimam diversificação associada,
entre outras coisas, às variáveis ambientais e a quantidade de linhagens do próprio clado
ao longo do tempo. Nós encontramos que os modelos de diversificação dependentes da
diversidade do próprio clado ao longo do tempo, que representam a competição intra-
clado, são melhores do que aqueles dependentes de variáveis ambientais. Nesse sentido,
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a competição entre linhagens por nichos disponíveis é mais importante para explicar a
dinâmica de diversidade de morcegos ao longo do Cenozóico do que o efeito direto de
processos ambientais ocorrendo em grandes escalas.
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Capítulo 1
Geographical idiosyncrasies on the relationship between environmental determinants
and bat species richness worldwide
Davi Mello Cunha Crescente Alves1, Kelly da Silva e Souza2, José Alexandre Felizola Diniz-
Filho3, Fabricio Villalobos3,4
1Programa de Pós-Graduação em Ecologia e Evolução, Universidade Federal de Goiás, CEP
74.001-970, Goiânia, Goiás, Brasil.
2Programa de Pós-Graduação em Genética e Biologia Molecular, Universidade Federal de
Goiás, CEP 74.001-970, Goiânia, Goiás, Brasil.
3Departamento de Ecologia, Universidade Federal de Goiás, CEP 74.001-970, Goiânia,
Goiás, Brasil.
4Red de Biología Evolutiva, Instituto de Ecología, A.C., Carretera Antigua a Coatepec 351,
El Haya, 91070 Xalapa, Veracruz, Mexico.
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Abstract
Geographical gradients of biodiversity are highly associated with distinct environmental
variables, but how such association varies worldwide at distinct spatial scales is poorly
understood. Here we used a spatial non-stationary model to partition the contribution of
different environmental hypotheses, including Energy, Spatial Heterogeneity and
Seasonality, in bat species richness patterns across the globe. We found that the shared
contributions among these hypotheses are more important than their specific
contributions and that such contributions vary considerably across the geographic space.
We conclude that the relationship between the environment and bat species richness is
more complex than previously thought, warranty the application of non-stationary models
that encompass different causal processes coupling local and global scales to understand
this complexity around the globe.
Keywords: Biogeography - Climate - GWR - Latitudinal Diversity Gradients - Non-
stationarity - Partial Regressions - SEVM - Spatial Models.
15
Introduction
One of the major questions in Ecology and Evolutionary Biology is why the tropics
has more variety of life forms than extratropical regions (Brown 2014). Several hypotheses
have been proposed to explain this general biodiversity pattern, usually involving multiple
ecological and evolutionary mechanisms occurring at different spatio-temporal scales, as
well as in multiple levels of the biological hierarchy (Mittelbach et al. 2007, Diniz-Filho and
Bini 2011). Among these hypotheses, those based on environmental variables, which
generally rely on topographic and climatic aspects of this multi-mechanism complexity
(Willig et al. 2003), are usually supported as playing a major role to maintain species
richness patterns (Hawkins et al. 2003, Rodriguez et al. 2005, Allen et al. 2007, Belmaker
and Jetz 2015).
The three principal environmental-based hypotheses posed to explain species
richness patterns are the Energy hypothesis, Environmental Heterogeneity hypothesis and
the Seasonality hypothesis (Tello and Stevens 2010). Regardless of their environmental
focus, basically these three hypotheses implicitly consider the two major sets of
underlying mechanisms, namelyecological and evolutionary processes. The Energy
hypothesis postulates that tropical regions are species rich because of high temperatures
and precipitation levels, consequently high net primary productivity. Because productivity
is associated with ecological resources availability, tropical regions supports high number
of individuals per species. This high abundance, in turn, results in more stable populations
over time and lower extinction rates (Hutchinson 1959, Currie et al. 2004). Moreover,
because tropical regions receive more energy, they present accelerated biological rates
16
from molecular mutations to speciation events (Rohde 1992, Allen et al. 2007). Now, the
Environmental Heterogeneity hypothesis postulates that tropical regions are species rich
because of their high amount of spatially structured environments. This spatial
heterogeneity allows the coexistence of several species per area (MacArthur 1964), as
well as a high probability of allopatric speciation (Simpson 1964, Tello and Stevens 2010).
Finally, the Seasonality or Climatic Stability hypothesis postulates that tropical regions are
species rich because they are climatically stable throughout multiple temporal scales.
Stable environments allow the coexistence of more ecologically specialized species
(Pianka 1966) and support lower extinction rates (Roy & Goldberg 2007). Despite
differences, some of the basic ecological and evolutionary mechanisms usually associated
with these hypotheses are similar.
Owing to the multiple causal processes driving geographical patterns of species
richness, a plausible analytical framework to identify such causes is one that considers the
contribution of different potential explanations instead of a framework seeking to find a
single, general explanation (Diniz-Filho et al. 2004, Stevens et al. 2011, Belmaker and Jetz
2015). For instance, Tello & Stevens (2010) analyzed the specific and shared contributions
of each of the aforementioned environmental hypotheses to explain bat species richness
across the New World. They found that the shared contributions of three hypotheses
were more important than the single contribution of any particular hypothesis or other
factors not included on the study (i.e. statistical residuals).
Besides geographical patterns of species richness can be explained by different
hypotheses, the particular explanatory power of each hypothesis could vary from one
17
geographical locality to another (Gouveia et al. 2013). Such phenomenon, known as
spatial non-stationarity, implies that the environment-richness relationship changes
across the geographic space with strong relationships characterizing some regions
whereas other regions present weak relationships (Fotheringham et al. 2002). Therefore,
explicitly considering such non-stationarity requires spatial models that estimate local
coefficients instead of models producing a global and unique coefficient for the whole
domain under study (Fotherigham et al 2002). Spatial non-stationary models, particularly
the Geographically Weighted Regression (GWR) has already been applied to explain
broad-scale species richness patterns for several groups such as amphibians (Cassemiro et
al. 2007, Gouveia et al. 2013), birds (Footy 2004, Osborne et al. 2007), palm trees
(Eiserhardt et al. 2011), and snakes (Terribile and Diniz-Filho 2009, Braga et al. 2014). For
instance, Gouveia et al. (2013) found with GWR that the shared contribution between
energy and seasonality was the best explanation for the worldwide amphibian species
richness pattern, but that energy and the shared contribution between energy and
heterogeneity were also important at particular regions.
One of the most conspicuous pattern of biodiversity is the global pattern of bat
species richness (Buckley et al. 2010; Figure 1). The order Chiroptera encompasses almost
1300 species distributed across all continents except Antarctica (Shi and Rabosky 2015,
Peixoto et al. 2013) and several studies have already confirmed the importance of the
environment shaping bat species richness at different scales (Stevens and Willig 2002,
Patten 2004, Buckley et al. 2010, Tello and Stevens 2010, Moura et al. 2016).
Nevertheless, to the extent of our knowledge, none of these studies used an analytical
18
framework allowing to test for spatial non-stationarity relationship between
multipleenvironmental determinants and bat species richness. Therefore, here we aim to
fill this gap by usingthe GWR framework to answer two questions: Is the global
environment-richness relationship of bats spatially non-stationary? How does the effect of
the environment, as well as the effect of each environmental hypothesis, upon bat species
richness varies worldwide?
Figure 1. Global pattern of bat species richness. Legend corresponds to the number of bat species
per 2º x 2º grid cell. Letters represent the zoogeographic realms (Holt et al. 2013): Na = Nearctic, P
= Panamanian, Nt = Neotropical, Pa = Palearctic, Sa = Saharo-Arabian, At = Afrotropical, M =
Madagascan, Or = Oriental, Au = Australian, Sj = Sino-Japanese, Oc = Oceanian.
19
Methods
Global pattern of bat species richness
We mappedthe geographical range of all bat species, which comprised a total of
1112species (IUCN 2013). With these data we constructed a global geographic
presence/absence matrix based on a grid of 2º x 2º degree cells.We choose this resolution
because is the one more suited to capture the effects of large-scale processes, such as
climatic variables, upon species richness at a global scale (Belmaker and Jetz 2011). We
only included grid cellsthat had an area overlap of 35% or morewith continents and we
excluded all the cells that had no species, leaving a total of 3214 cellsand 831 species
(Figure 1).
Environmental variables
To select all the variables used to represent each environmental hypothesis, we
followed Tello and Stevens (2010). Accordingly, the Energy hypothesis was represented by
mean temperature, annual precipitation and Net Primary Productivity (NPP). The
Environmental heterogeneity hypothesis was represented by the standard deviation of
mean temperature, precipitation, NPP and elevation in each grid cell. Note that the
measure of statisticdispersion of these variables represents their spatial variation within a
2º x 2º grid cell. Finally, the Seasonality hypothesis was represented by the standard
deviation of temperature and the coefficient of variation of precipitation along time. Note
that the measures of statistic dispersion of these variables represent their variation per
year within a 2º x 2º grid cell. Temperature, precipitation and elevation layers were
20
obtained from WorldClim (2015) and NPP from Imhoff eta l. (2004). Given that all of these
variables had lower resolutions than our 2º grid, we scaled them up to this resolution
before applying subsequent analyses.
Analyses
To answer the first question – Is the global environment-richness relationship of
bats spatially non-stationary? - we compared two spatial models: one that assumes
stationarity (Spatial Eigenvector Regression Maps; SEVM) and other that do not (GWR).
We used both models to analyze the effect of the nine environmental variables upon bat
species richness worldwide and compared them using different Akaike Information
Criterion metrics (AIC; Burnham and Anderson 2002). A SEVM model is similar to an
Ordinary Least Square model to evaluate the effect of the environment upon species
richness, except for the fact that it uses spatial eigenvectors (or filters) to take into
account the spatial structure on model residuals (Diniz-Filho and Bini 2005). To generate
these spatial filters, we used the longest truncation distance of the geographic distance
matrix which keeps all the grid cells connected. We selected 28 spatial filters based on the
minimum number of filters that decreased the autocorrelation of the residuals - between
richness as response variable and environmental variables and spatial filters as
explanatory variables - below an Moran's I of 0.05 in the first distance class.
Contrary to the SEVM model, which is a "global" model, the GWR model estimates
OLS coefficients for each grid cell in the geographic domain (Fotheringam et al. 2002). To
do so, the GWR model uses a pool of cells surrounding each focal cell in the geographic
21
domain to make an OLS between the environmental variables and species richness within
the region defined by such pool of cells (Fotheringham et al. 2002). Thus, in our case, we
did a total of 3214 locals OLS. To determine which and how many cells will be considered
in each local OLS, we used an adaptive spatial kernel that varies between 10-15% of the
neighborhood cells and uses the set of cells that minimizes the AIC. To minimize the
spatial autocorrelation on model's residuals between the neighborhood cells and the focal
cell, we used a Bi-square spatial function to weight the neighborhood cells according to
their distance to the focal cell (Fotheringam et al. 2002).
We also evaluated SEVM and GWR models by analyzing the spatial structure on their
residuals at different geographical scales. We used Moran's I as the autocorrelation
statistic and 20 classes of spatial distance (with mean distance between classes of ~ 300
kilometers) with the same number of cells pairs. Positive spatial autocorrelation at a given
distance class means that the cells pair at that scale are more similar than expected for a
cells pair randomly taken at any distance class. Conversely, negative spatial
autocorrelation at a given distance class means that the cells pair at that scale are more
dissimilar than expected for a cells pair randomly taken at any distance class.
To answer the other questions - How does the effect of the environment, as well as
the effect of each environmental hypothesis, upon bat species richness varies worldwide?-
we estimated and mapped the coefficient of determination (R2) of the GWR model based
on all the nine environmental variables aforementioned for each cell in the globe. This
coefficient estimates the proportion of variability in the response variable that are
attributed to the explanatory variables and we interpreted it as how much the
22
environment explains the bat species richness pattern in each locality in the globe. Then,
following Gouveia et al. (2013), we did several partial GWR, which are similar to partial
multiple regressions, to estimate partial R2 for each set of explanatory variables for each
cell in the globe. These partial R2 were: specific to energy (E), specific to heterogeneity (H),
specific to seasonality (S), and the shared contribution between energy and heterogeneity
(E:H), energy and seasonality (E:S), heterogeneity and seasonality (H:S), as well as the
contribution shared among energy, heterogeneity and seasonality (E:H:S; see Legendre &
Legendre 2012 for details on partial regression).
All analyzes were conducted using the SAM software version 4 (Rangel et al. 2010)
and the "letsR" (Vilela and Villalobos 2015) and "vegan" (Oksanen et al. 2015) packages of
the R environment (R Development Core Team, 2016).
Results
The global environment-richness relationship for bats is non-stationary, as shown by
the better fit of the GWR model compared to the SEVM model (GWR; AICw= 1; Table 1).
Also, the GWR model wasbetter than the SEVM model in controlling the spatial structure
of model residuals over different geographical scales (Figure 2).
Table 1. Comparison between a stationary (SEVM) and a non-stationary (GWR) spatial model to
explain the global bat species richness pattern. N = number of parameters, LogLik = logLikelihood,
AICc = corrected Akaike Information Criterion, ΔAIC = delta AIC, and AICw = Akaike weights.
23
Models N LogLik AICc ΔAIC AICw
Stationary 38 -10591.68
21259.35
1328.164
0
Non-stationary 182 -9783.593 19931.186 0 1
Figure 2. Correlogram plots depicting spatial autocorrelation of the residuals from a spatial
stationary model (SEVM) and from a spatial non-stationary model (GWR). Confidence intervals
(95%) not shown because they were lower than 4 x 10-3units of I'Moran for all distance classes.
The mean distance between distance classes (x-axis) was ~300 km.
24
Based on the GWR model results, we found that the environment has a strong effect
upon bat species richness across almost all regions of the globe (mean R2across grid cells =
0.79, Figure 3, Figure 4), with some exceptions being regions at the southeast of the
Afrotropical and Madagascan realms and at the middle of the Palearctic realm. Moreover,
the effect by each environmental determinant, and, thus, the explanatory power of each
environmental hypothesis, upon bat species richness varied considerably across the globe
(Figure 5, Table 2). The environmental determinant that explained most of the bat species
richness gradient was the shared contributionbetween Energy : Heterogeneity :
Seasonality (E : H : S component; Table 2), followed by the shared contribution of Energy :
Seasonality (E : S component), the specific contribution of Energy (E component) and the
shared contribution of Energy : Heterogeneity (E : H component). All the other specific and
shared contributions of environmental determinants presented low explanatory power for
the geographic pattern (Table 2). In the same vein, the shared contribution of the E : H : S
componentshowed high explanatory power across most of the Neotropical, Panamanian,
Nearctic, Sino-Japanese, Oriental, Oceanian and Australian realms and some parts of the
Afrotropical, Saharo-Arabian and Palearctic realms. Moreover, the shared contribution of
the E : S component had high explanatory power in most of the Neotropical and
Afrotropical realms and some parts of the Sino-Japanese and Oriental realms. The specific
contribution of the Energy hypothesis had high explanation in most of the Madagascan
and Palearctic realms, whereas the shared contribution of the E : H hypothesis had high
explanation only across the Saharo-Arabian realm.
25
Figure 3. Distribution of coefficients of determination (R2) of GWR for the analysis of bat species
richness regressed on 9 environmental variables.
26
Figure 4. Spatial non-stationarity on the effect (R2) of the three environmental hypotheses and
their combination posed to explain the global bat species richness pattern.
Figure 5. Spatial variation on the partial coefficients of determination (R2) for three environmental
hypotheses and their shared effects. The coefficients are: specific to energy (E), specific to
heterogeneity (H), specific to seasonality (S), shared contribution between energy and
heterogeneity (E:H), energy and seasonality (E:S), heterogeneity and seasonality (H:S), as
well as the contribution shared among energy, heterogeneity and seasonality (E:H:S).
27
Table 2. Mean standardized coefficient of determination (R2) for each environmental hypothesis
and their shared contributions influencing the global bat species richness pattern. The coefficients
are related to energy (E), heterogeneity (H), seasonality (S), energy and heterogeneity (E:H),
seasonality and energy (S:E), heterogeneity and seasonality (H:S), energy and heterogeneity and
seasonality (E:H:S).
E H S E : H S : E H : S E : H : S
R2 (± 1
SD)
0.19 (±
0.17)
0.06 (±
0.05)
0.02 (±
0.02)
0.1 (±
0.13)
0.20 (±
0.15)
0.04 (±
0.07)
0.38 (±
0.20)
Discussion
Energy, environmental heterogeneity and seasonality are well known environmental
determinants shaping broad-scales biodiversity patterns (Willig et al. 2003, Hawkins et al.
2003, Currie et al. 2004), including bat species richness (Patten 2004, Tello and Stevens
2010, Buckley et al. 2010, Moura et al. 2016). Here, we took one step further by showing
that the relationship between these environmental determinants and bat species richness
is not constant across the globe. In addition, we showed that the shared effect of all these
three environmental determinants upon bat species richness is more important than their
specific effects.
Our results show that the environment-richness relationship for bats is non-
stationary across the globe as different regions exhibited distinct strengths of such
relationship (Table 1). Despite the fact that the GWR model included a higher number
28
ofparameters than the SEVM model, the former model presented a way much better fit to
the bat species richness pattern than the latter. Our findings, together withresults from
several other studies conducted with different animal and plant taxa (see Footy et al.
[2004] and Eiserhardt et al. [2011]), stress the necessity to compared spatial models that
estimate local coefficients with those that estimate a unique, global set of coefficients
when studying broad scale biodiversity gradients.
The environment is a good explanation for bat species richness for almost the entire
globe (Figure 3-4). Accordingly, such effect of the environment on bat species richness
was consistently large across almost all biogeographic realms, including those with high
biodiversity such as the Neotropical and Panamanian realms. It is important to note that
the well documented environment-richness relationship discussed on the literature (see
Field et al. [2009] and references therein) is different from the one we discussed here. The
former relationship represents how the global environment explains the global species
richness pattern of spatially stationary models estimating a unique R2. Conversely, our
consideration of the environment-richness relationship represents how a regional
environment, delineated by the environmental features of the pool of neighborhood
localities surrounding a focal locality, explains the regional species richness of that pool of
localities. And, how this relationship between regional environments and regional species
richness varies across the globe. Furthermore, in our case, model residuals attributed to
each locality do not correspond to the difference between the observed and estimated
species richness for that locality given the environmental model, as is the case when using
stationary spatial models such as SEVM which includes all localities in the globe. Instead,
29
within the GWR framework, model residuals attributed to each locality represents the
proportion of species richness variation within the pool of neighboring localities (and not
all localities as in the SEVM framework) that is not associated with that regional
environment.
What does it mean to find a high explanatory power of the environment for bat
species richness at different regions of the world? In short, it means that the
environmental properties of these regions are sufficient to explain bat species richness
without resourcing to other unaccounted variables. Because we discuss each
environmental hypothesis in detail below, we now focus on the spatial distribution of our
local model residuals, which are the regions for which local environment-richness
relationships had low explanatory power (Figure 4). Most regions with high model
residuals are concentrated on islands, such as in the Madagascan and Oriental realms, and
surrounding great lakes, as the lake Malawi in the Afrotropical realm and the lake Baikal in
the Palearctic realm. We speculate thatthis pattern of model residuals for islands is
determined mainly by water barriers constraining bat's dispersal, even though bats have
high dispersal capabilities owing to their flight adaptations, or by other microevolutionary
events that we are not aware of. For both great lakes, we speculate that the high
concentration of residuals are determined mainly by the fact they are nearby the limits of
bat's geographic ranges; i.e. the Indic ocean and the North Pole. These geographic
constrains in addition to the magnitude of the great lakes might caused an artifact on the
selection of the neighborhood cells concerning the focal cells at these regions. Because we
used an adaptive spatial kernel to sample the neighborhood cells at these regions, the
30
sample cells are probably too far from each other and occupy very different
environments, which masked the environment-richness relationship at these high residual
localities.
To move forward, we believe is necessary to explicitly define here the term "effect"
employed along this paper (e.g. the effect of the environment upon species richness). On
the one hand, the term "effect" can be expressed as the regression coefficient between
regional environments and regional species richness across a certain geographic domain.
For example, Cassemiro et al. (2007) demonstrated that the regression coefficients
between temperature and amphibian species richness varies across the geography. In
other words, they estimated the absolute effect of temperature upon amphibians at
different regions, which can be mechanistically understood as the number of amphibian
species "generated" by temperature at different regions. On the other hand, in our case,
we used the term "effect" as the coefficient of determination between regional
environments and regional species richness across the globe. Thus, because we estimated
the proportion of species richness variation that is attributed to the environment, we are
interpreting a relative effect (and not an absolute effect) of a regional environment upon
bat species richness on a particular region. Consequently, as our environment-richness
relationship is non-stationary, we assumed that this relative "effect" of the environment
changes across the geographic space.
The specific and shared effects of the environmental determinants upon bat species
richness presented considerable geographic structure, with their shared effects being
more important than their specific effects (Figure 5). The importance of different
31
environmental determinants acting together to influence species richness patterns has
been recently shown for different vertebrate taxa (Gouveia et al. 2013, Moura et al. 2016).
Particularly for bats, Tello and Stevens (2010) found that the shared contribution of
energy, heterogeneity and seasonality (E : H : S component) followed by that of energy
and seasonality (E : S component) were the most important drivers of the species richness
geographic gradient of New World bats. Our findings support those of Tello and Stevens,
highlighting the potentially pervasive effect of all these environmental determinants
combinedin driving bat species richness gradients in general across the entire globe and
particularly within specific regions of it.
In our case, the shared effect of different environmental hypotheses upon the global
pattern of bat species richness can be the result of correlationsamong some of the
variables considered between the hypotheses (see these correlations in the Appendix 1).
For example, energy-like variables are in general negatively correlated with seasonality-
like variables and positively correlated with heterogeneity-like variables. In an extreme
sense, this non-independence or collinearity amongenvironmental variables has been
interpreted as an unsolvable statistical problem (Gouveia et al. 2013), but can also be
understood as the intrinsic nature of the environmental determinants driving the
geographic patterns. For instance, these correlations may indicate that high energy
regions, such as in the tropics, have low energy variation over time but a high energy
variation across space. Such spatio-temporal variation provides insightful information to
understand bat species richness.
32
Energy is an important driver of species richness (Currie et al. 2004, Belmaker and
Jetz 2015) and our results reinforce this statement (Figure 5). However, energy alone has a
high specific effect upon bat species richness only at regions with low species richness
(Figure 1) and with high residuals considering all environmental variables together (Figure
4), such as in the Palearctic and Madagascan realms. In fact, energy is only a major driver
of bat species richness at high bat species rich regions, such as at the tropics, when mean
energy-like variables associate with energy-like variables that vary across time and
geography. This means that regions that presents high bat species richness present the
following environments: i) high energy but low temporal energy variation (E : S
component), or ii) high energy but low temporal variation and high geographic variation (E
: H : S component). Conversely, regions with low bat species richness, such as at
temperate regions, presents an environment with low energy geographic variation but
high energy temporal variation (H : S component). Therefore, we highlight the necessity to
look at the correlation of the environmental variables between hypotheses to understand
shared effects, because their signals might be very important to understand how each
environmental determinant affects the species richness pattern worldwide.
We demonstrated here that the relationship between the environment and bat
species richness presents geographical idiosyncrasies. The environment is an important
driver of bat species richness across most of the globe, but at some regions, such as
islands, dispersal barriers may affect how the number of species is particularly linked to
the environment. We also demonstrated that the shared effects of different aspects of the
environment are more important to determine bat species richness than their specific
33
effects. And that looking at the signal of their correlations provides very insightful
information about geographic patterns. The relationship of the environment with
biodiversity is not a trivial task, consequently, the useof non-stationary models which
encompasses a multitude of causal processes is one step forward to help us understand
this complexity worldwide.
Acknowledgments
DMCCA and KSS received a studentship from the Coordenação de Aperfeiçoamento
de Pessoal de Nível Superior (CAPES). JAFD-F has been continuously supported by CNPq
productivity grants. FV was supported by a BJT “Science without Borders” grant from
CNPq.
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40
Capítulo 2.1
Geographical diversification and the effect of model and data inadequacies: the bat
diversity gradient as a case study*
Davi Mello Cunha Crescente Alves1,*, José Alexandre Felizola Diniz-Filho2 and Fabricio
Villalobos2,3
1Programa de Pós-Graduação em Ecologia e Evolução, Universidade Federal de Goiás, CEP
74.001-970, Goiânia, Goiás, Brasil.
2Departamento de Ecologia, Universidade Federal de Goiás, CEP 74.001-970, Goiânia,
Goiás, Brasil.
3Red de Biología Evolutiva, Instituto de Ecología, A.C., Carretera Antigua a Coatepec 351,
El Haya, 91070 Xalapa, Veracruz, Mexico.
*Correspondence: Davi M. C. C. Alves,Departamento de Ecologia, Universidade Federal de
Goiás, CEP 74.001-970, Goiânia, Goiás, Brasil;
E-mail: [email protected].
*Artigo aceito para publicação na revista "Biological Journal of the Linnean Society".
41
Abstract
The adequacy of some promising phylogenetic comparative methods to test for trait-
dependent diversification has been recently criticized to suffer from inflated Type 1 Error
rates (i.e. model inadequacy). Nevertheless, formal tests of this inadequacy for such
models within an explicit geographical context are still missing as well as tests of other
types of inadequacies such as those related to geographic and phylogenetic data (i.e. data
inadequacies). Here, we take advantage of the striking geographic diversity gradient
exhibited by bats to explicitly test whether inferences derived from the "geographic-state,
speciation and extinction" model (GeoSSE) are biased by model and data inadequacies.
We used uncertainty, sensitivity and simulation analyses to show that GeoSSE is sensitive
to data inadequacies, being more affected by geographical than phylogenetic
inadequacies. Moreover, as previously suggested, the GeoSSE model also suffers from
inflated Type 1 Error rates. Our results indicate that the GeoSSE model is not reliable for
inferring the relative roles of evolutionary processes in driving the bat latitudinal diversity
gradient. We argue that uncertainty, sensitivity and simulation analyses should be
conducted in all comparative studies that associate species traits and diversification
processes to understand diversity gradients.
Keywords:Character - Commission Error - Macroevolution - Phylogenetic Uncertainty -
Species Richness - SSE models
42
Introduction
The global species richness of mammals presents the ubiquitous latitudinal diversity
gradient (LDG) with a decrease in species numbers from the tropics to the poles (Willig,
Kaufman & Stevens, 2003). Although most mammalian orders present such species
richness gradient, bats are the main taxon determining the LDG of the whole mammalian
class (Kaufman, 1995; Buckley et al., 2010). Therefore, explaining the LDG for bats may not
only help to understand the causes driving the mammalian LDG but those of diversity
gradients in general since such causes are likely to operate in other taxa as well (Willig et
al., 2003; Buckley et al., 2010; Jablonski et al., 2017). Such explanation requires the explicit
consideration of the macroevolutionary processes that directly change species numbers:
diversification, which is the balance between speciation and extinction, and dispersal
(Ricklefs, 2004). Indeed, different evolutionary hypotheses regarding such processes have
been proposed to explain large-scale diversity gradients (Mittelbach et al., 2007; Brown,
2014). Thanks to the increasing availability of time-calibrated phylogenies and
phylogenetic comparative methods, it is now possible to estimate the rates of
macroevolutionary processes and thus discriminate among such evolutionary hypotheses
(Pyron & Burbrink, 2013; Morlon, 2014).
For instance, the Tropical Niche Conservatism (TNC; Wiens & Donoghue, 2004) and
the Out of the Tropics hypotheses (OTT; Jablonski, Roy & Valentine, 2006) are the two
main hypotheses advanced to explain the mammalian LDG (Buckley et al., 2010; Rolland
et al., 2014). TNC posits that most clades originated in the tropics, occupying it longer and
rarely dispersing out of it, thus accumulating more species in that region without implying
43
differences on macroevolutionary rates between tropical and extratropical regions (Wiens
& Donoghue, 2004). Whereas OTT also posits a tropical origin of clades but with higher
speciation and dispersal and lower extinction rates in the tropics than in extratropical
regions (Jablonski et al. 2006). For bats, TNC has been favored with studies supporting its
predictions on their richness gradient; e.g. higher richness of early diverged species in the
tropics and strong positive temperature-richness relationship (Stevens, 2006; 2011;
Buckley et al., 2010). However, a recent study considering all mammals contrasted these
two hypotheses and found more support for OTT in most orders, including bats (Rolland et
al., 2014). Although findings were mostly similar among mammalian orders, some showed
contrasting results altogether (e.g. Carnivora) or differences depending on model
specifications (e.g. support vs no support for OTT in Chiroptera) (Rolland et al., 2014). In
fact, contrasting results arising from different model specifications may be related to
inherent assumptions and biases of phylogenetic comparative methods (Cooper, Thomas
& FitzJohn, 2016).
Despite initial excitement on phylogenetic comparative methods that model
macroevolutionary processes (so-called ‘diversification models’; Morlon, 2014), several of
these methods have been recently criticized and even deemed unreliable (Maddison &
FitzJohn, 2015; Rabosky & Goldberg, 2015; Cooper et al., 2016; Moore et al., 2016). For
example, the ground breaking model proposed by Maddison, Midford & Otto (2007) that
relates the state of a two-state discrete species trait to speciation and extinction rates
("binary state speciation-extinction" model, BiSSE) has been shown to be highly sensitive
to model violations such as pseudoreplication (Maddison & FitzJohn, 2015) and spurious
44
correlations between a focal trait and diversification rates (Rabosky & Goldberg, 2015).
This is particularly important for studies on geographic diversity gradients since the
geographical extension of such model ("geographic state speciation-extinction" model,
GeoSSE; Goldberg, Lancaster & Ree, 2011), in which macroevolutionary (speciation,
extinction and dispersal) rates are associated to particular regions (e.g. tropics vs
temperate), may suffer from the same issues as the BiSSE model. The GeoSSE model has
been widely applied to assess the influence of macroevolutionary processes in
determining the geographic diversity gradients of different taxa (Jansson et al., 2013),
from plants (Goldberg et al., 2011; Staggemeier et al., 2015), birds (Pulido-Santacruz &
Weir, 2016) and reptiles (Pyron, 2014) to the abovementioned study of mammals (Rolland
et al., 2014). Hence, a critical open question is to what extent model assumptions and
biases affect inferences from the GeoSSE model.
The most important problem of these state dependent speciation-extinction
models (xxSSE; FitzJohn, 2012) is potentially inferring an association between a species
trait and macroevolutionary rates when in fact none exists (model inadequacy, Rabosky &
Goldberg, 2015). This problem could induce inflated Type I Error rates, rendering xxSSE
models inadequate for testing evolutionary hypotheses (Rabosky & Goldberg, 2015). In
addition, uncertainties related to the data used to fit such models (e.g. trait
measurements and species’ phylogenetic relationships) can also affect the performance of
xxSSE models. Regarding the GeoSSE model, such data inadequacies (Figure 1) can come
from the designation of species membership to particular geographic regions, which is
based both on defining such regions and identifying the region (s) within which each
45
species occurs (Goldberg et al., 2011; Figure 1A and Figure 1B, respectively) as well as
from the phylogenetic uncertainties such as polytomies (Figure 1C).
Figure 1. Diagram representing the three types of data inadequacies which could affect inferences
from the GeoSSE model for geographic gradients of biodiversity. a) Represents two regionalization
schemes to categorize the globe into tropical and extratropical regions, one based on latitude
(superior dotted line: 23.4º N, inferior dotted line: -23.4º S) and another based on environmental
productivity (dark gray = tropics; white = extratropics). b) Represents the commission error on the
geographic range of a hypothetical species (elipse) that is endemic to the tropics (white rectangle)
46
but might be considered transtropical because 5% of its range mistakenly overlaps the extratropics
(gray rectangle). c) Represents the generation of two dichotomic phylogenetic trees owning to the
"break" of the polytomy of the original phylogenetic tree.
Here, we evaluate the influence of model and data inadequacies on inferences
derived from the GeoSSE model by means of uncertainty, sensitivity and simulation
analyses. We focus on large-scale species richness gradients and the discrimination among
evolutionary hypotheses explaining such gradients. For this, we used the striking
latitudinal diversity gradient exhibited by bats. As previously stated, bats are widely used
to understand geographic diversity gradients given their high diversity (~1300 species),
broad occupation of almost all terrestrial habitats and the considerable amount of
phylogenetic and geographic information available for this group (Jones et al., 2002; Willig
et al., 2003; Buckley et al., 2010; Peixoto et al., 2013; Shi & Rabosky, 2015). Moreover,
several studies had already applied diversification models to understand bats’
evolutionary history (Jones et al., 2005; Yu et al., 2014; Shi &Rabosky, 2015), including the
GeoSSE model (Rolland et al., 2014), which allows comparison with our findings. Specific
results for bats under the GeoSSE model showed contrasting results between constrained
and unconstrained dispersal parameters (Rolland et al., 2014) with the former supporting
the OTT hypothesis whereas the latter supporting a reverse trend with lower tropical
diversification compared to extratropical regions and higher dispersal from these into the
tropics. We show that, at least for bats, such findings and thus supporting a particular
evolutionary hypothesis using the GeoSSE model can be heavily dependent on geographic,
47
and less so on phylogenetic, uncertainties of the input data in addition to suggested
model inadequacies.
Methods
The GeoSSE approach and data inadequacies
The GeoSSE model is a trait-dependent diversification model, based on the likelihood-
based framework of Maddison et al. (2007), that uses reconstructed phylogenies of extant
species and in which speciation and extinction rates are influenced by the values of a
particular species trait (Goldberg et al., 2011). Contrary to the original BiSSE model, where
such macroevolutionary rates are tied to the binary trait state (e.g. phenotypic or life
history), in GeoSSE the trait is the geographic location of species and thus
macroevolutionary rates are tied to both geographic regions where species occur. In
addition, a species can occupy one of the two region or occupy both regions. Finally, state
transitions in GeoSSE represent range dynamics of dispersal (expansion) and local
extirpation (contraction) (Goldberg et al., 2011). Therefore, GeoSSE requires phylogenetic
and distributional information of species as input data.
Geographic data inadequacies
Geographic data for GeoSSE comes directly from the distribution of species, either
from point occurrences (e.g. Goldberg et al. 2011) or range maps (e.g. Rolland et al.,
2014). Such information is then used to define the membership of species to particular
regions. For example, in the context of the LDG, species need to be assigned to a
48
particular region such as tropical (t, occurring exclusively within the Tropics), extratropical
(e, occurring exclusively within regions out of the Tropics) or transtropical (te, occurring
over both regions). Defining the geographic membership of species to such regions
requires two steps: i) determine which regions across the globe are tropical and which are
extratropical; and ii) identify the region(s) within which each species occurs. The first step
can be done in different ways, where most GeoSSE studies have used latitude to
categorize the globe into tropical and extratropical regions (e.g. ±23.4º; Figure 1A;
Jansson, Rodríguez-Castañeda & Harding, 2013; Rolland et al., 2014). However, this
latitude-based regionalization may be too coarse to define tropical and extratropical
regions. For instance, some regions characterized by low average temperature and
precipitation are environmentally similar to extratropical regions (<-23.4º or >23.4º) but
are considered tropical under a regionalization strictly based on latitude. This is the case
of the Mediterranean Forests, Woodlands and Scrubs ecoregion that occurs on high
elevations of the Central Andes in South America (Olson et al., 2001). Similarly, some
regions characterized by high average temperature and precipitation are environmentally
similar to tropical regions (> -23.4º and <23.4º) but are considered extratropical under a
regionalization strictly based on latitude, such as the Flooded Grasslands and Savannas
ecoregion (i.e. Everglades) in southeast North America (Olson et al., 2001).
At large spatial scales, such as those used for studying LDGs, range maps are usually
the norm for geographic data (Hurlbert & Jetz, 2007). Consequently, the second step in
defining species membership to a given geographic trait state for GeoSSE - i.e. identifying
the region (s) within which each species occurs - is generally done by overlapping species
49
range maps onto tropical and extratropical regions (e.g. Rolland et al., 2014). Range maps
represent a coarse model of species geographic distributions and are generated either by
experts, which based on their knowledge of species determine the regions where the
species can occur, or by simply tracing a minimum convex polygon around the most
disperse occurrence points known for each species (IUCN 2001). On the one hand, range
maps tend to be more efficient to reduce omission errors - incorrectly inferring that a
species does not occur in a given region - than other geographic data such as point
occurrences or species distribution models (Rondinini et al., 2006). On the other hand,
range maps unfortunately tend to increase commission errors - incorrectly inferring that a
species occurs in a given region (Figure 1B; Rondinini et al. 2006; Hurlbert & Jetz, 2007;
LaSorte & Hawkins, 2007). Under the GeoSSE framework, commission errors could have
drastic consequences on the definition of species membership to a given region. For
example, if a species is actually adapted to tropical regions but 1% of its range is
mistakenly considered to be within extratropical regions, this species will be categorized
as transtropical. Hence, if there is a high number of species that are actually adapted to a
particular region but their geographic distribution presents commission errors on the
tropical-extratropical transition, the amount of transtropical species could be considerably
inflated.
Phylogenetic data inadequacy
Phylogenetic data for GeoSSE, and xxSSE models in general, relies on time-
calibrated dichotomic resolved phylogenies. However, such phylogenies can suffer from
several uncertainties from topology to temporal calibration (Diniz-Filho et al., 2013). For
50
instance, in molecular phylogenies, topological uncertainties such as polytomies can be
introduced by the posterior inclusion of species with no molecular data (Rangel et al.,
2015). One way to handle such phylogenetic uncertainty on diversification analyses is to
break polytomies using, for instance, birth-death models (Kuhn, Moers & Thomas, 2011)
and then use the resultant set of phylogenies in the analyses (Rolland et al., 2014).
Nevertheless, there is no consensus on whether this procedure bias the inferences made
by phylogenetic comparative methods when estimating diversification rates (Kuhn et al.,
2011; Rabosky, 2015). For example, it has been suggested (but not tested) that breaking
polytomies under a birth-death model might bias inferences made by trait-dependent
diversification models given that the inclusion of non-sampled species is not random with
respect to the trait distribution among the tips of the phylogeny (Rabosky, 2015).
Geographic and Phylogenetic data of Bats
We obtained information on bat species phylogenetic relationships from a widely used
species-level and time-calibrated supertree of mammals provided by Bininda-Edmonds et
al. (2007) and based on Jones et al. (2002, 2005) for bats. This supertree was updated by
Fritz et al. (2009) and contains sequence data for 1054 bat species. Information on the
geographic distribution of bats was obtained from range maps available on the IUCN
online database (IUCN, 2014) and, when necessary, we complemented these with
information from Wilson & Reeder (2005). There were 1140 species with available
geographic data and we used this information to determine species membership to
tropical, extratropical or transtropical regions across the globe. We adopted the
taxonomic classification of Wilson & Reeder (2005) and we corrected for all synonyms.
51
Handling data inadequacies
Handling geographic data inadequacies
The first step before applying the GeoSSE model to bat data was to determine species
membership to one (tropical, extratropical) or both regions (transtropical) across the
globe. To deal with the problem of a regionalization scheme solely based on latitude, we
generated two alternative regionalizations (i.e. type of traits; hereafter, TRAIT; Figure 1A).
The first TRAIT was the traditional one based on latitude (hereafter, GEO-TRAIT). For GEO-
TRAIT, we overlaid the range maps of all bat species on a global map and identified
whether a species occurred within the tropical region (i.e. > -23.4º and <23.4º),
extratropical region (i.e. <-23.4º or> 23.4º) or within both regions. Following Jansson et al.
(2013), we coded species as “t” (tropical), “e” (extratropical) and “te” (transtropical).
The second TRAIT was based on an environmental variable (hereafter, ENV-TRAIT;
Figure 1A). We assumed productivity - the amount of biomass in an ecosystem - as the
main environmental variable characterizing tropical and extratropical regions, given that
high productivity regions are commonly associated with tropical biomes, whereas low
productivity regions are usually associated with extratropical biomes (Hawkins et al.,
2003). We used Actual Evapo-Transpiration (hereafter, AET) as a proxy for productivity.
From a set of productivity-like variables such as Net Primary Productivity and the
bioclimatic variables derived from temperature and precipitation, AET was the only one
that satisfactorily separated high productive regions, such as tropical humid forests, from
low productive regions, such as deserts or high mountain tops (maps not shown). We used
a raster file with AET values on a resolution of 0.25º as provided by UNEP (2014).
52
Because AET is a continuous variable, we had to transform it into a binary variable to
delineate the two regions: tropical and extratropical. We used a k-means clustering
method (Legendre & Legendre 2012) to divide the globe, using the raster cells, into two
regions. This k-means method applies an algorithm to cluster the cells into two groups and
identify the cluster that minimizes the difference between the cells within each group
(Legendre & Legendre 2012). We randomly clustered the cells 20 times and used 1000
iterations for each clustering to relocate the cells between the two groups and calculate
the within-group residual sum of squares. Finally, to determine species membership to
each region based on ENV-TRAIT, we overlaid the range maps of all bat species with a
global map of productivity and identified whether a species occurred in a tropical (i.e. high
productivity), extratropical (i.e. low productivity) or in both regions. Species were coded in
the same way as for the GEO-TRAIT (t, e and te).
Once regions were defined, the second step was to determine the membership of
species to each or both regions. To do so, we used range maps that, as mentioned above,
may contain commission errors that could inflate the number of transtropical species
(Figure 1B). To deal with this problem, we generated range thresholds (hereafter, RANGE),
which consisted in the percentage of species range area in km2 overlapping the
extratropical region. We established 21 range thresholds, ranging from 0 to 20%. Thus, at
one end of the spectrum, if we assumed a RANGE of 0%, all species with 0% of their range
area overlapping the extratropical region were considered tropical and all species with
100% were considered extratropical. Accordingly, species with 1 to 99% of their range
area overlapping the extratropical region were considered transtropical. At the other end
53
of the spectrum, if we assumed a RANGE of 20%, all species with ≤ 20% of their range area
overlapping with the extratropical region were considered tropical and all species ≥ 80%
were considered extratropical. In the same vein, species with 21 to 79% of their range
area overlapping the extratropical region were considered as transtropical.
We assumed range thresholds of 0 to 20% because there is empirical evidence
suggesting a minimum threshold of 20% to realistically consider sympatry between
species range (see Price et al. [2014] and references therein), which could also be used to
represent commission errors between species range and its occurrence within a region.
We opted to not consider higher range thresholds because this could inflate the number
of endemic species, instead of inflating the number of transtropical species.
Handling phylogenetic data inadequacy
The original phylogenetic supertree of mammals, from which we obtained the
phylogenetic relationships among bats, presents several polytomies generated by
inserting species with no genetic data on the phylogeny (Jones et al., 2005; Bininda-
Emonds et al., 2007). To address the uncertainty generated by the breaking of such
polytomies in our analyses, we used 100 dichotomic pseudoposterior phylogenies
provided by Kuhn et al. (2011). These trees were built using a birth-death model to
randomly insert the missing species on the phylogeny, given all the taxonomic information
available to minimize the error associated with this species input. In addition, we used a
maximum clade credibility tree analysis to identify the bat phylogeny with the most
common topology among the 100 pseudoposterior phylogenies (MCC phylogeny;
Drummond et al., 2012).
54
GeoSSE application to bats LDG
We applied the GeoSSE model (Goldberg et al., 2011) to estimate speciation, extinction
and dispersal rates of bats from tropical and extratropical regions. Each parameter is
associated to a region and these can be: speciation (St, Se or Ste), extinction (Xt or Xe) and
dispersal (Dt or De). GeoSSE requires two inputs: a phylogeny and a trait vector
representing species membership to the regions. In our case, we used several phylogenies
to consider phylogenetic uncertainty and trait vectors representing our two
regionalization schemes as well as different range thresholds. We randomly selected a
sample of 10 phylogenies (PHYs) out of the 100 resolved phylogenies obtained from Kuhn
et al. (2011; see explanation above). Given that we had two regionalizations (TRAIT) and
21 range thresholds (RANGE), we worked with a total of 42 trait vectors. Therefore, we
had 420 combinations of phylogenies and trait vectors (10 phylogenies x 42 trait vectors;
hereafter, phy-geo data). Considering all these phy-geo data, we ran the unconstrained
GeoSSE model (i.e. all parameters free to vary) for each data. Given that the considered
phylogenies were incomplete with regard to the total number of recognized bat species,
we used a correction function for the GeoSSE model, as provided in the diversitree
package, to associate the missing species with the available trait states (FitzJohn,
Maddison & Otto, 2009).
Uncertainty Analysis
To quantify the level of uncertainty in GeoSSE parameters associated with geographic and
phylogenetic data inadequacies, we partitioned the total parameters variance across all
three potential sources of uncertainty represented by our different data: TRAIT, RANGE
55
and PHY (for a similar approach, see Diniz-Filho et al., 2009; Rangel et al., 2015). To do so,
we used a PERMANOVA (Anderson, 2001) to understand how much of the variation in
GeoSSE parameters (i.e. St, Se, Ste, Xt, Xe, Dt, De) was associated with TRAIT (two levels:
ENV or GEO) and RANGE (21 levels: 0-20% thresholds; Figure 2). We used PHY as
replicates, hence, the residuals of the PERMANOVA were associated with the differences
across phylogenies generated by the polytomy resolution. We evaluated each factor
separately (TRAIT or RANGE) as well as their interaction (TRAIT*RANGE). To avoid
replicate dependency among treatments, we randomly sampled for each treatment 10
PHYs out of the 100 available PHYs, leaving a total of 420 replicates (i.e. 10 replicates per
treatment). We used the mean square of each factor to identify how much each of them
contributed to the total parameters variation (Gotelli & Ellison, 2004).
56
Figure 2. Variance partition of GeoSSE parameters. There were 420 GeoSSE results for the
unconstrained model (one for each phy-geo data combination). ENV = environmental; GEO =
geographical; PHY = phylogenetic component or residuals; RANGE = range threshold; TRAIT =
regionalization type; and * = interactions.
Sensitivity analysis
To determine the effect of geographic data inadequacies on the inferences derived from
the GeoSSE model, we evaluated the support of GeoSSE results for a particular hypothesis
explaining the LDG (a brief explanation of each hypothesis is given in Appendix 2). To do
so, we followed two steps: i) express the most common evolutionary hypotheses for the
57
LDG in terms of GeoSSE macroevolutionary parameters (Table 1) and, then, ii) associate
GeoSSE results (parameters) with the corresponding hypotheses. Based on this
hypotheses-parameter association, sensitivity to geographic data inadequacies was
identified as the variation of such association as a function of TRAIT and RANGE factors.
Evolutionary hypotheses to explain the latitudinal diversity gradient can be easily
expressed in terms of GeoSSE parameters (Table 1). We considered 9 such hypotheses
whose underlying mechanisms could be explicitly associated with the macroevolutionary
parameters for each region obtained with the GeoSSE model (for an example of such
association, see Roy & Goldberg, 2007). Based on this hypotheses-parameters association,
we only considered the GeoSSE results for the MCC tree. Thus, we were able to associate
each of our 42 GeoSSE results - one for each TRAIT and RANGE - with each of the 9
evolutionary hypotheses considered. Note that these hypotheses do not contemplate all
parameter combinations, thus some GeoSSE results could not be associated with any
hypothesis.
Table1. Association between macroevolutionary parameters of the GeoSSE model with traditional
hypotheses explaining the latitudinal diversity gradient. D = dispersal; e = extratropical region; S =
speciation; t = tropical region; X = extinction.
Model Hypotheses Speciation Extinction Dispersal
1 Pure dispersal St = Se Xt = Xe Dt < De
2 Macroevolutionary St >Se Xt = Xe Dt > De
58
source-sink
3 Evolutionary speed St > Se Xt = Xe Dt = De
4 Environmental Stability St = Se Xt < Xe Dt ≥ De
5 Out ofthe Tropics St > Se Xt < Xe Dt > De
61 Tropical Niche Conservatism St = Se Xt = Xe Dt = De
72 Into The Tropics 1 St > Se Xt < Xe Dt < De
83 Into The Tropics 2 St = Se Xt > Xe Dt < De
94 Into The Tropics 3 St < Se Xt < Xe Dt < De
1 This hypothesis also assumes that the values of dispersal are low; 2 See Pyron and Wiens 2013 for
amphibians; 3 See Rolland et al. 2014 for an unconstrained model used for bats (see their
supplementary information); 4See Pyron 2014 for squamates.
Simulation analysis
To test model inadequacy of GeoSSE, we first simulated a "null hypothesis" scenario of no
association between trait and macroevolutionary parameters (Rabosky & Goldberg, 2015).
For the “null hypothesis” scenario, we simulated 100 phylogenies with the same number
of species as our empirical bat phylogeny under a pure-birth process. Next, on each
phylogeny, we simulated a neutral trait evolving under a continuous-time discrete-state
Markov process. To account for the effect of these neutral traits evolving at different
rates, we simulated these traits at four rates (q): 0.05, 0.1, 1 and 10 (Rabosky & Goldberg,
2015). Then, we reshuffled the trait states across the tips to generate random species
values. Thus, we simulated the phylogenies as well as random traits to create a
conservative "null hypothesis" scenario of no association between trait and
59
macroevolutionary parameters (Burin et al., 2016). Later, we fitted two GeoSSE models to
each simulation dataset: i) a null model where speciation and extinction were constrained
to be equal across character states (St = Se; Xt = Xe) while dispersal was potentially
asymmetric (Dt De), and ii) an alternative model where extinction rates were
constrained to be equal across states (Xt = Xe) but speciation and dispersal rates were
potentially asymmetric (St Se; Dt De). Then, we used a likelihood-ratio test (LRT) with
significance level of 0.05 to compare model fits. Because our “null hypothesis” scenario
simulated no association between trait and macroevolutionary parameters, we
considered an inflated Type 1 error rate of the GeoSSE model if the best fit model for the
simulated data were the asymmetric parameter model; i.e. the alternative model
described above. To account for other less conservative "null hypothesis" scenarios, we
also tested GeoSSE for model inadequacy by simulating random and neutral traits under
bat's empirical phylogenies (Appendix 2).
We performed all the analyses in R (version 3.2.3) using the following packages: ape
(Paradis, Claude & Strimmer, 2004), diversitree (FitzJohn, 2012), geiger (Harmon et al.,
2008), phytools (Revell, 2012) and vegan (Oksanen et al., 2015). R code for assessing Type
1 Error rates is available in Appendix 2.
Results
Our principal aim was to conduct different sets of analyses to evaluate the influence
of data and model inadequacies on the inferences derived from the GeoSSE model for the
latitudinal diversity gradient of bats. Our first analysis evaluated uncertainty as the effect
of data inadequacies on the variability of GeoSSE model parameters. Indeed, this
60
uncertainty analysis showed that the variance of GeoSSE results is mostly explained by
geographic data inadequacies rather than phylogenetic data inadequacies. The factor that
contributed the most to parameters variation was RANGE (40.8%), followed by
TRAIT*RANGE (33%), TRAIT (16.1%) and PHY (10.1%).
Our second analysis evaluated the sensitivity of inferences derived from GeoSSE -
support for an evolutionary hypothesis - to geographic data inadequacies. This sensitivity
analysis showed that supporting a particular evolutionary hypothesis is greatly affected by
geographic data inadequacies (Table 2). Considering the environmental regionalization
(ENV-TRAIT), 20 GeoSSE results (95,2%) supported the Out of the Tropics hypothesis and
only one result supported a parameter combination not considered in our stated
hypotheses. Conversely, considering GEO-TRAIT, 66.6% of the GeoSSE results supported
parameter combinations not considered in our hypothesis (14 results), 14.3% of the
results supported the Into the Tropics 3 hypothesis (4 results), 9.5% of the results
supported the Out of the Tropics hypothesis (2 results), and only one result supported the
Into the Tropics 2 hypothesis (Table 2).
Table 2. Different explanations for the global pattern of bat species richness and how their support
by GeoSSE varied according to trait (environmental or geographical) and range thresholds (0-20%).
Black areas represent GeoSSE results that support a given hypothesis according to trait and range
threshold.
Range Thresholds 0 1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19 20
61
(%)
Hypotheses Environmental Trait
Pure dispersal
Source-sink
Evol. Speed
Stability
Out-Tropics
Conservatism
Into-Tropics 1
Into-Tropics 2
Into-Tropics 3
No Hyp.
GeographicalTrait
Pure dispersal
Source-sink
Evol. Speed
Stability
Out-Tropics
Conservatism
Into-Tropics 1
Into-Tropics 2
Into-Tropics 3
No Hyp.
62
Finally, our last analysis evaluated whether the GeoSSE model systematically infers a
misleading incorrect association between geographic occurrences and diversification
rates. This simulation analysis showed that GeoSSE model suffers from inflated Type 1
Error rates (Figure 3). In fact, the GeoSSE model showed inflated Type 1 Error rates for all
rates in which the simulated random traits evolved: 48% for q = 0.05; 37% for q = 0.1; and
20% for both q = 1 and q = 10. Therefore, even when the disassociation between trait and
macroevolutionary rates increased as the trait evolved more rapidly - higher q rates, the
GeoSSE model still presented inflated Type 1 Error rates. Moreover, GeoSSE model also
presented inflated Type 1 Error rates for the others "null hypothesis" scenarios (Figures 1
and 2 in the Appendix 2).
63
Figure 3. Test of model inadequacy for GeoSSE model. We simulated 100 phylogenies under a
pure-birth process, and for each of them, we simulated a random trait. We repeated this process
for traits evolving at four transition rates (q = 0.05, q = 0.1, q = 1 and q = 10). We used the "
Likelihood ratio test" to contrast a null and alternative GeoSSE models and evaluate whether
GeoSSE incorrectly rejected the null hypothesis of no association between trait and speciation
rate. Red dotted lines represent the significance level of 0.05.
Discussion
Several hypotheses have been put forward to explain the latitudinal diversity gradient in
terms of ecological and evolutionary processes (Pianka, 1960; Mittelbach et al., 2007;
Brown, 2014). Compared to ecological processes, evaluating the influence of evolutionary
processes has exploded in recent years thanks to the availability of phylogenetic
information and comparative methods (Morlon, 2014). However, critical evaluation of
such advances, particularly methodological ones, is needed to guarantee the adequacy of
data and models used to infer the causes behind diversity patterns (Rabosky & Goldberg,
2015; Cooper et al., 2016). We have highlighted the need for such critical evaluation when
using a geographical diversification model to support evolutionary hypotheses explaining
the LDG. Using the striking LDG exhibited by bats as an example, we showed that the
"geographic state speciation-extinction" model (GeoSSE) is not only affected by model
inadequacy, as previously suggested for the BiSSE model (Rabosky & Goldberg, 2015) but
also by data inadequacies, namely geographic and phylogenetic. Such model and data
64
inadequacies can severely bias our inferences, potentially leading us to support an
incorrect evolutionary hypothesis.
The type of data inadequacy that most affected the GeoSSE model was the way in
which species membership was assigned to a particular region (RANGE, in our
terminology; Figure 3). This suggests that studies that have used GeoSSE to understand
geographical gradients of species richness for groups such as amphibians, mammals and
squamates (Pyron & Wiens, 2013; Rolland et al., 2014; Pyron, 2014), might have reached
biased conclusions (but see Pulido-Santacruz & Weir [2016] for an exception). For
instance, a recent study of mammals (Rolland et al., 2014) applied the GeoSSE model
under a geographical regionalization (GEO-TRAIT, in our terminology) and no restriction
on range overlap (RANGE of 0%, in our terminology) to define species membership to
tropical and extratropical regions. Particularly for bats, this study found that both regions
had the same speciation rate but different extinction and dispersal rates, with higher
extinction in tropical regions and higher dispersal from the extratropics into the tropics
(Rolland et al., 2014; based on the unconstrained GeoSSE model). In our analysis, using
similar geographic and phylogenetic data as well as model specifications (unconstrained
dispersal) as Rolland et al. (2014) for bats, we were able to support the same explanation
(i.e. Into the Tropics 2 hypothesis) only under GEO-TRAIT and RANGE of 5% (Table 2). This
finding implies that our interpretation of the evolutionary processes responsible for the
bat LDG is highly dependent on geographic data, mainly the level of commission error
assumed in the analysis.
65
The notion that commission errors associated with range maps can mask the
understanding of geographic patterns of biodiversity is not new (Hurbelt & Jetz, 2007; La
Sorte & Hawkins, 2007). Recently, different studies have explicitly considered this data
inadequacy in their analyses by validating, assuming or testing range thresholds. For
instance, Tobias et al. (2014) established a threshold of 20% of breeding range overlap
among ovenbird species to determine whether they were sympatric (>20% of range
overlap) or allopatric (< 20% of range overlap). This threshold was validated by a
systematic revision of published species range maps and point occurrences (Tobias et al.,
2014). Other authors incorporated commission errors in their analyses by assuming a
unique threshold of 25% of latitudinal range overlap with tropical and extratropical
regions; e.g. a species was considered tropical only if more than 75% of its range was
tropical (Kerkhoff, Moriarty & Weiser, 2014). And recently, Pulido-Santacruz & Weir
(2016) tested RANGEs of 5%, 10%, 15% and 20% for birds on GeoSSE and found no
significant differences across their results. This latter study further suggested that the
sensitivity of GeoSSE to RANGE might be clade-specific. Therefore, whenever accurate
geographic data to determine species membership to a given region is missing, different
RANGEs should be considered when applying and interpreting results from geographic-
dependent diversification models.
After the range threshold factor (RANGE), the data inadequacy that most affected
GeoSSE was the way in which we categorized the globe into tropical and extratropical
regions (TRAIT, in our terminology; Table 2). In our results, both regionalizations (TRAITs)
were associated with different evolutionary hypotheses explaining the LDG of bats. When
66
considering the environmental regionalization (ENV-TRAIT), results were associated with
two hypotheses, whereas using the geographical regionalization (GEO-TRAIT) associated
the results with four hypotheses. A possible explanation for such distinct inferences from
the choice of regionalization is that the environmental regionalization produces regions
that are more fragmented and detailed given that environmental variables, such as
primary productivity, are heterogeneously distributed on geographic space (Figure 1A).
Consequently, a more fragmented regionalization produced, on average, a greater
amount of transtropical species (Figure 3 in Appendix 2), which in turn reduced the
parameter variance across the different range thresholds (RANGEs). This parameter
consistency across RANGEs favored the support of fewer hypothesis by GeoSSE. Thus,
explicitly considering the environment in delineating different regions seems to be a more
reliable scheme for inferences derived from diversification analyzes.
Phylogenetic data inadequacy had a lower effect on the variation of GeoSSE
parameters than geographic data inadequacies. Our results contradict the expectation
that polytomy resolution based on birth-death models could bias inferences from trait-
dependent diversification models (Rabosky, 2015). Other studies had already shown no
significant biases in diversification patterns owing to phylogenetic uncertainty after
breaking polytomies (Kuhn et al., 2011; Rolland et al., 2014). For instance, Rolland et al.
(2014) found that speciation and extinction rates for several mammalian orders were
consistent across their pseudoposterior trees. Thus, we believe that phylogenetic
uncertainty caused by the polytomy resolution might not considerably affect inferences
made by trait-dependent diversification analyses. Even so, these findings may be clade-
67
specific and future studies should be conducted to test the generality of this potentially
negligible effect of phylogenetic uncertainty on diversification analyses.
Our findings suggest that the GeoSSE model, as it has been implemented so far,
does not provide fully reliable tests of alternative evolutionary hypotheses (Figure 3). This
model showed inflated Type 1 Error rates in our conservative "null hypothesis" scenario,
which presented a high level of disassociation between trait and diversification rates,
implying that the GeoSSE model is prone to associate diversification differences with traits
that did not cause such differences. Such spurious correlations are also consistent across
less conservative "null hypothesis" scenarios based on empirical bat phylogenies with
neutral and random traits (Figures 1 and 2 in Appendix 2). Thus, our results reinforce
Rabosky & Goldberg’s (2015) expectation that SSE models (BiSSE, ClaSSE, GeoSSE, MuSSE,
QuaSSE and etc.) might be inadequate to test evolutionary hypotheses. Some possible
solutions to overcome this model inadequacy is to use a statistical procedure to correlate
lineage-specific diversification rates - generated by a trait-independent model - with a
biological trait (Rabosky & Huateng, 2015; but see Moore et al. 2016), or to use a trait-
dependent model that includes hidden states in the analyses (HiSSE; Beaulieu & O'Meara,
2016). A drawback of the latter solution is that the model was built for traits that present
only two known states. Therefore, the HiSSE model cannot be used, in its current form, to
understand the LDG because species geographic membership requires three trait states:
tropical, extratropical and transtropical.
Aside from data and model inadequacies, other concerns need to be taken into
account when using SSE models to understand geographic diversity gradients. One
68
important issue is the linkage between evolutionary hypotheses and GeoSSE results
highlighted in this study (Table 1). Some hypotheses have additional components than
simply speciation, extinction and dispersal. For instance, the Tropical Niche Conservatism
hypothesis posits that the elapsed time also contributes to the species richness pattern
(“time-for-speciation" effect), given that the Tropics are older than extratropical regions
thus having more time to accumulate species (Wiens & Donoghue, 2004; see Appendix 2).
This effect, however, cannot be explicitly tested with GeoSSE. Therefore, alternative
methods to SSE models are still needed to test all of the components posit by evolutionary
hypotheses to explain geographic diversity gradients.
Conclusions
We demonstrated here that the use of a trait-dependent diversification model to
understand geographic patterns of biodiversity is highly biased by data and model
inadequacies. Geographic data inadequacies related to the definition of tropical and
extratropical regions as well as commission errors of species geographic distributions
affect inferences made by the geographical SSE model more than phylogenetic
uncertainty. Moreover, as expected, the geographical SSE model demonstrated to be
inadequate to test evolutionary hypotheses owing to inflated Type 1 Error rates. These
evidences illustrate how problematic SSE models can be to understand geographic
diversity gradients. We highlight that the use of uncertainty, sensitivity and simulation
analyses to evaluate data and model inadequacies should not be restricted only to the use
of SSE models within a geographical context, but to all comparative studies that associate
69
phylogenies with causal factors (e.g. biological traits or abiotic variables) to understand
biodiversity patterns.
Acknowledgments
We are indebted to Lucas Jardim for helpful comments on the manuscript and Luciano F.
Sgarbi for optimizing the R codes. We also thank Folmer Bokma, John A. Allen, Sebastian
Höhna, Tanja Stadler and two anonymous reviewers for helpful comments on a previous
version of this manuscript. DMCCA received a studentship from the Coordenação de
Aperfeiçoamento de Pessoal de Nível Superior (CAPES). JAFD-F has been continuously
supported by CNPq productivity grants. FV was supported by a BJT “Science without
Borders” grant from CNPq.
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Capítulo 2.2
Testing the statistical performance of a geographical trait-dependent diversification
model: a comment on Pulido-Santacruz and Weir (2016)
Davi M. C. C. Alves1,*, Jesus N. Pinto-Ledezma1, Luciano F. Sgarbi1, José A. F. Diniz-Filho2&
Fabricio Villalobos2,3
1 Programa de Pós-Graduação em Ecologia e Evolução, Departamento de Ecologia,
Instituto de Ciências Biológicas, Universidade Federal de Goiás, CP 131, CEP 74001-970,
Goiânia, Goiás, Brazil.
2 Departamento de Ecologia, Instituto de Ciências Biológicas, Universidade Federal de
Goiás, CP 131, CEP 74001-970, Goiânia, Goiás, Brazil.
3 Red de Biología Evolutiva, Instituto de Ecología, A.C., Carretera antigua a Coatepec 351,
El Haya, 91070 Xalapa, Veracruz, Mexico.
* e-mail: [email protected]
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Abstract
Pulido-Santacruz and Weir (2016) applied a trait-dependent diversification model (ClaSSE)
to explain avian species richness patterns at broad geographic scales and found that
extinction was the principal process driving those patterns. However, ClaSSE-like models
have recently been criticized from suffering high Type I Error rates, and, indeed, Pulido-
Santacruz and Weir (PW) conducted statistical performance analyses and showed no
considerable problems with ClaSSE. But, as we discuss here, their performance analyses
do not seem to be the more appropriate methods to explicitly test ClaSSE for Type I Error.
Therefore, we complemented their analyzes by conducting three different simulation
analyses to explicitly evaluate their ClaSSE model for statistical error. We simulated in
each analysis a scenario of no association of trait with diversification rate, and, then, we
fitted a trait-independent and a trait-dependent diversification model. All of our results
supported the trait-dependent model, which suggests that the ClaSSE model, as
implemented by PW, has a poor statistical performance. Hence, we advocate that ClaSSE
model alone might not be a good approach to evaluate geographic patterns of species
richness and warn against general conclusions derived solely by trait-dependent
diversification models.
Keywords: Model adequacy, SSE-models, type I error, speciation, phylogenetic
comparative methods.
79
Introduction
Geographic variation in species richness is ultimately caused by evolutionary processes
such as speciation, extinction, and dispersal (Rolland et al., 2014). In their recent study,
Pulido-Santacruz and Weir (2016; hereafter, PW) showed that higher avian richness in
tropical regions is better explained by lowest extinction, rather than higher speciation or
dispersal rates, compared to temperate regions. These macroevolutionary rates were
estimated by applying a trait-dependent diversification model known as ClaSSE (Goldberg
and Igic 2012) to an extensive phylogenetic and geographic avian dataset. ClaSSE is part of
a widely used set of "state, speciation and extinction" models (SSE) that have recently
been criticized for suffering inflated type I errors rates (Rabosky and Goldberg 2015).
More specifically, Rabosky and Goldberg (2015) proposed a set of performance analyses
to evaluate SSE models and showed that they tend to infer an association between
diversification and a given biological trait even when this association does not exist.
Unfortunately, Rabosky and Goldberg evaluated only the statistical performance of
a simple two-states SSE model (BiSSE; Maddison et al. 2007), leaving aside more complex
models such as ClaSSE. Aware of these issue, PW created two analyses to evaluate the
statistical performance of their multi-state ClaSSE model. In their first analysis, they
compared the parameters (i.e. rates) used to simulate the data with the parameters
estimated from this simulated data. If there was no considerable difference, the model
was assumed to present a good performance because it was able to recover the original
parameter values. More specifically, PW took the median ClaSSE parameters fitted to their
Maximum Clade Credibility (MCC) avian phylogeny and use them to simulate 300
80
phylogenies with their associated geographic trait data. Each geographic trait contained
seven states regarding New World low latitude, New World high latitude, Old World low
latitude, Old World high latitude, New World mixed, Old World mixed and Holartic region.
Then, they fitted a ClaSSE model to each simulated phylogeny-trait dataset and compared
the median parameters across simulations with their actual estimates. Their results
showed no considerable differences on parameters between both datasets, thus
supporting a good performance of their model.
In their second analysis, PW evaluated ClaSSE performance by comparing
speciation, extinction and dispersal (estimated upon an empirical phylogeny and neutral
traits) between two states. If there were no considerable parameter differences between
the two states, the model has a good performance given that the analysis was built under
the premise of no association between parameters and traits. To do this, they simulated
1000 neutral binary traits on the MCC avian phylogeny, where half of simulations started
with one state at the root node, and the other half with the other state. Then, they used
the BiSSE model (Maddison et al. 2007) to estimate the parameters to each simulated trait
and the MCC phylogeny (see Appendix 2 in PW). According to this analysis, PW concluded
that their results showed no considerable parameter differences between states, thus,
also supporting a good performance of their model. PW’s main justification to use a BiSSE
model to evaluate ClaSSE performance was that there is no method available to simulate a
seven-character state along a phylogeny in a way that is consistent with the ClaSSE
assumption.
81
However, both analyses created by PW did not explicitly tested ClaSSE for Type I
Error. Their analyses did not simulate a "null hypothesis" scenario of no association
between trait and diversification rates with a subsequent comparison between a trait-
independent diversification model (null model) and a trait-dependent diversification
model (alternative model). Therefore, to complement the performance analyses
conducted by PW, we explicitly evaluated the ClaSSE model for Type I Error. To do so, we
simulated three different datasets to reproduce the "null hypothesis" scenario of no
association between trait and diversification rate and then use a null ClaSSE model to
contrast it against an alternative ClaSSE model. These datasets were simulated as follows:
1) using an empirical phylogeny and simulating neutral traits (EN dataset); 2) using an
empirical phylogeny and simulating random traits (ER dataset), and 3) using a simulated
phylogeny and simulating random traits (SR dataset). More specifically, for the EN and ER
dataset, we used the MCC avian phylogeny (6670 spp.; only with genetic data) to
stochastically simulate 100 neutral and random trait values for the tips, respectively.
Neutral traits contained seven states and were simulated under a continuous-time
discrete state Markov process with a transition rate of 1. To generate random state values
for the tips, we reshuffled the tips among the seven states for each neutral trait. For the
SR dataset, we simulated a phylogeny under a pure-birth process with the same number
of species as the MCC avian phylogeny and then generated 100 random values for the
tips. We only used simulated traits with the proportion of species per state greater than
0.08, because, given the number of states, it was not possible to satisfy the threshold of
0.1 of species per state originally proposed by Davis et al. (2013) to avoid Type II error. We
82
relaxed this assumption to avoid inflated Type II error given that our goal was to test only
for Type I error.
We fitted a null and an alternative ClaSSE model for each of the 100 simulations
of our three datasets. For our null model, we restricted speciation (λ), extinction (μ), and
allowed some dispersal parameters (d) to vary according to PW. This set of parameters
constrains characterized a trait-independent diversification model. For our alternative
model, we allowed some speciation and dispersal parameters to vary according to PW,
but we constrained extinction. This set of parameters constrains characterized a trait-
dependent diversification model. Because likelihoods were computed for both null and
alternative models, we calculated their Likelihood Ratio Test (LRT) as well as the
probability of this statistic under a 2 distribution for each simulation of each dataset,
adopting a critical significance level of 5% (Rabosky and Goldberg 2015). If the majority of
simulations from each dataset wrongly rejected the null hypothesis, the ClaSSE model was
considered to present high Type I error rates because it inferred an association between
trait and speciation rate where there was none (Rabosky and Goldberg 2015). Conversely,
if the majority of simulations from each dataset correctly accepted the null hypothesis,
the ClaSSE model was considered to have low Type I error rates because it correctly
inferred no association between trait and speciation rate. To account for the difference on
the number of parameters between the null and alternative models, we also computed
the difference in AIC between these models for each simulation (Burnham and Anderson
2002). If the AIC differences were negative, then, an inflated type I error was found for the
ClaSSE model. We used the Language and Statistical Environment R (R Core Team, 2015)
83
and the R packages diversitree (FitzJohn 2012) and phytools (Revell 2012) to evaluate
ClaSSE statistical performance (R scripts available on Appendix 2.2).
Our results show that the ClaSSE model, as implemented by PW and in our
simulations, is potentially prone to inflated Type I Error (Fig. 1). In fact, all of our
simulations for the three datasets wrongly rejected the null hypothesis of no association
between trait and speciation rate (Fig. 1A-C). Moreover, when taking into account the
number of parameters of both models with the AIC, all simulations for the three datasets
also supported the alternative model rather than the null model (Fig. 1D-F). As expected,
the third dataset (SR), in which the disassociation between trait and speciation rate was
more controlled, presented a shorter average distance between the alternative and null
model in terms of AIC.
84
Figure 1. Type I errors rates for ClaSSE model under EN, ER and SR datasets. The histograms A), B)
and C) shown the frequency of the probability of the LRT statistics under a 2 distribution for 100
simulations, for EN, ER and SR datasets, respectively. The arrows indicate a critical significance
level of 5%. The x-axis (P-values) was log-transformed for best viewing. The histograms D), E) and
F) shown the frequency of the AIC difference between the alternative and the null ClaSSE model
for 100 simulations, for EN, ER and SR datasets, respectively.
Our analyses on the statistical performance of the ClaSSE model complement
those conducted by PW. However, our results contrast with theirs and revealed that such
model does not have a high statistical performance as originally proposed by PW. On the
one hand, their results are in accordance with a recent study which aimed to detect an
association between avian diet and diversification rate (Burin et al. 2016). Burin and
colleagues conducted several analyses to evaluate the statistical performance of a multi-
state SSE model as complex as ClaSSE and did not find any considerable issue. However, as
PW, they did not test their SSE model explicitly for Type I Error as we did here. On the
other hand, our results are in accordance with Rabosky and Goldberg (2015)'s overall
expectation that SSE models suffer from model inadequacy. They showed that BiSSE
model is prone to inflated Type I Error datasets with empirical phylogenies (including
Birds) with different simulated traits (neutral and random values for the tips). However,
Rabosky and Goldberg did not find inflated Type I Errors for datasets with simulated
phylogenies with simulated traits. Therefore, it seems that SSE models could show either
good or bad performance depending on the models being studied, the dataset to simulate
the "null hypothesis" scenario and the framework for testing Type I Error rate. This, in
85
turn, stresses once again the importance of explicitly diagnosing SSE model adequacy for
every study (Rabosky and Goldberg 2015).
Our framework can also be considered as a complement to the study of Rabosky
and Goldberg (2015). They conducted performance analyses and provided code only for
the evaluation of the BiSSE model, which is a two-state trait-dependent diversification
model. Moreover, Rabosky and Goldberg only applied the complete phylogenetic and trait
simulations (EN, ER and SR dataset as we did here) on the Cetacean clade. For the Bird
clade, they only simulated neutral traits on empirical trees (EN dataset), which does not
seem to be the more appropriate method to simulate a "null hypothesis" scenario of no
association between trait and diversification rate (Burin et al. 2016). To foster a more
comprehensive evaluation of such SSE models, we here provide code (Appendix 2.2) to
conduct performance analyses for the multi-state ClaSSE model with different simulation
scenarios (EN, ER, and SR).
Finally, our findings cast doubt on the potential role of extinction in driving avian
latitudinal diversity gradients as suggested by Pulido-Santacruz and Wier (2016). Even so,
we believe that their ecological and evolutionary interpretations cannot be challenged
solely on the basis of the low performance of their ClaSSE model (and they actually
support previous analyses with much simpler approaches; e.g. Hawkins et al. 2006).
Nevertheless, we do warn against general conclusions derived from trait-dependent
diversification methods alone. Further investigations are still necessary to better establish
the appropriate methods that can reliably inform us about the drivers of geographical
diversity gradients under a macroevolutionary perspective. We hope that our proposed
86
framework (and code) may foster more appropriate assessments of Type I error rates in
diversification models that depend on discrete traits with several states.
ACKNOWLEDGEMENTS
DMCCA, JNPL, and LFS received a studentship from the Coordenação de Aperfeiçoamento
de Pessoal de Nível Superior (CAPES). JAFD-F has been continuously supported by CNPq
productivity grants. FV was supported by a BJT “Science without Borders” grant from
CNPq.
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Omnivory in birds is a macroevolutionary sink. Nature Comm. 7:1-10.
Burnham, K. P., & D. Anderson. 2003. Model selection and multi-model inference. A
Pratical informatio-theoric approch. 2nd edition. Springer-Verlag, New York.
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estimation of the BiSSE method for analyzing species diversification. BMC Evol. Biol.
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FitzJohn, R. G. 2012. Diversitree: Comparative phylogenetic analyses of diversification in R.
Methods Ecol. Evol. 3:1084–1092.
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Evolution. 66:3701–3709.
Hawkins, B. A., J. A. F. Diniz-Filho, C. A. Jaramillo, and S. A. Soeller. 2006. Post-Eocene
climate change, niche conservatism, and the latitudinal diversity gradient of New
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Maddison, W. P., P. E. Midford, and S. P. Otto. 2007. Estimating a binary character’s effect
on speciation and extinction. Syst. Biol. 56:701–710.
Pulido-Santacruz, P., and J. T. Weir. 2016. Extinction as a driver of diversity gradients.
Evolution. 70:860–872.
Rabosky, D. L., and E. E. Goldberg. 2015. Model Inadequacy and Mistaken Inferences of
Trait-Dependent Speciation. Syst. Biol. 64:340–355.
Revell, L. J. 2012. phytools: An R package for phylogenetic comparative biology (and other
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88
Capítulo 3
Integrating Selection, Niche and Diversification into a Hierarchical Conceptual
Framework*
Davi Mello Cunha Crescente Alves1,*, José Alexandre Felizola Diniz-Filho2and Fabricio
Villalobos2,3
1Programa de Pós-Graduação em Ecologia e Evolução, Universidade Federal de Goiás, CEP
74.001-970, Goiânia, Goiás, Brasil.
2Departamento de Ecologia, Universidade Federal de Goiás, CEP 74.001-970, Goiânia,
Goiás, Brasil.
3Red de Biología Evolutiva, Instituto de Ecología, A.C., Carretera Antigua a Coatepec 351,
El Haya, 91070 Xalapa, Veracruz, Mexico.
*Correspondence: Davi M. C. C. Alves,Departamento de Ecologia, Universidade Federal de
Goiás, CEP 74.001-970, Goiânia, Goiás, Brasil;
E-mail: [email protected].
*Artigo publicado na revista "Organisms Diversity and Evolution".
89
Abstract
Recently, new phylogenetic comparative methods have been proposed to test for the
association of biological traits with diversification patterns, with species ecological ‘niche’
being one of the most studied traits. In general, these methods implicitly assume natural
selection acting at the species level, thus implying the mechanism of species selection.
However, natural selection acting at the organismal level could also influence
diversification patterns (i.e. effect-macroevolution). Owing to our scarce knowledge on
multi-level selection regarding niche as a trait, we propose a conceptual model to discuss
and guide the test between species selection and effect macroevolution within a
hierarchical framework. We first assume niche as an organismal as well as a species’ trait
that interact with the environment and results in species-level differential fitness. Then,
we argue that niche heritability, a requirement for natural selection, can be assessed by its
phylogenetic signal. Finally, we propose several predictions that can be tested in the
future by disentangling both types of evolutionary processes (species selection or effect-
macroevolution). Our framework can have important implications for guiding analyses
that aim to understand the hierarchical perspective of evolution.
Keywords: Individual-based models - Niche conservatism - Macroevolution - Phylogenetic
comparative methods - SSE models - Species selection - Trait.
90
Introduction
After the Modern Evolutionary Synthesis that unified the ideas of Mendel and Darwin in
the 1930’s and 1940’s, evolutionary dynamics through deep-time began to be thoroughly
discussed under the mechanism of natural selection (Simpson 1944). Their focus was to
explain macroevolutionary patterns as a result of within-species, microevolutionary
processes (Gould 1982). However, some authors questioned this classic darwinian
perspective of selective process acting at the organismal level, considering it insufficient
to explain all the macroevolutionary patterns, and suggested an expansion to the Modern
Synthesis (Eldredge and Gould1972). One aspect of this expansion was based on a
hierarchical view of evolution, which considers processes acting at different levels of
biological organization and emphasizes the effects of scale and hierarchy to improve our
understanding of the history of life (Gould 1982; Jablonski 2007).
Organic evolution by means of natural selection could happen through the
environment selecting organisms with certain traits (Darwin 1859), which is traditionally
understood as a population-level process. However, such Darwinian mechanism could also
happen at any level of the biological hierarchy, from genes to higher taxa, given that
certain conditions are met (Jablonski 2008). This hierarchical expansion of the
evolutionary theory is logically possible if the units of selection can be shown to have
traits presenting three basic criteria: i) variability; ii) heritability, and iii) interaction with
the environment resulting in differential reproduction (Lewontin 1970).
Under this view, selective process could happen at the species level (i.e. species
selection) if species present traits that are variable, heritable, and promote differential
91
speciation and/or extinction across lineages (Stanley 1975; Rabosky and McCune 2009).
Although theoretically possible and increasingly accepted, there is still ample debate
around species selection as an evolutionary force, with two main topics of debate:
whether species’ traits can be downscaled to the organismal level and whether
diversification patterns result from microevolutionary or macroevolutionary processes
(Lieberman and Vrba 2005; Jablonski 2008; Myers and Saupe 2013). The first issue
revolves around the consideration of species’ traits as “aggregated” organismal traits or as
traits exclusively “emerging” at the species level (Lloyd and Gould 1993). On the one hand,
aggregate traits can be represented as descriptive statistics (e.g. sum or mean) of a certain
organisms' trait of a given species, with some examples being body size, dispersal
capabilities or trophic levels (Jablonski 2008). On the other hand, emergent traits are
species’ traits that only occur at the species level and cannot be summarized by
descriptive statistics of organisms' traits; some examples are geographic range, sex ratio
and genetic population structure (Jablonski 2008).
The other debate on whether diversification patterns are mediated by
microevolutionary and/or macroevolutionary processes hinges on the distinction between
upward and downward causations (Lieberman and Vrba 2005). Upward causation
represents the selective process acting over organism level traits that influence
diversification at the species level, a process also known as effect-macroevolution (Vrba
and Eldredge 1984). An example of effect-macroevolution can be the interaction of the
environment with organism’s body size determining differential diversification across
lineages (Jablonski 2008).However, is important to highlight that upward causation will
92
not always necessarily affect species-level evolution (Vrba and Gould 1986). Downward
causation, on the contrary, represents selective process acting upon species traits that
influence diversification at the species level as well as birth and death rates at the
organismal level. This process is also known as “strict-sense” species selection (hereafter,
simply species selection; Jablonski 2008). An example of species selection can be the
interaction of the environment with species’ geographic range resulting in differential
diversification across lineages (Vrba and Gould 1986; Jablonski 1987).
A first attempt to disentangle between effect-macroevolution and species selection
is to determine whether the biological trait under selection is aggregated or emergent
(Jablonski 2008). If the trait is aggregated, effect-macroevolution is more likely the main
macroevolutionary process. Otherwise, if the trait is classified as emergent, species
selection must be necessarily the main evolutionary process behind macroevolutionary
patterns (Jablonski 2008). However, it is possible that a given aggregated trait that
increases organism level fitness could also decrease species-level fitness, or the other way
around (see Diniz-Filho 2004). That is, an asymmetry between levels may arise from the
interaction of different-level traits with the environment. An example of this “cross-level”
conflict could happen with body size. Large organisms are traditionally assumed to
present increased fitness owing to higher competing capabilities and/or environmental
tolerances than smaller organisms (Maurer 1998). At the same time, species composed by
large organisms require larger areas to satisfy their energetic needs and maintain viable
populations compared to small organisms (Marquet and Taper 1998). Consequently,
species composed by large organisms may have higher chances of extinction under a
93
fluctuating environment than species with small organisms (Diniz-Filho 2004). Therefore,
we believe that disentangling effect-macroevolution from species selection is not as
straightforward as simply defining whether a species’ trait can be reduced or not to the
organism level.
Recently, with the advancement of phylogenetic comparative methods, several
models have been formulated to test for statistical associations between biological traits
and differential speciation and/or extinction (Maddison et al. 2007; Pyron et al. 2013;
Morlon 2014; see a critic to these methods in Rabosky and Goldberg 2015). However, the
majority of studies using such trait-dependent diversification models have not explicitly
discussed the above-mentioned topics such as trait reducibility, selection at different
levels or cross-level conflicts (but see Goldberg et al. 2010). For instance, some studies
have tested for an association between ecological niches and diversification patterns
(Kozak and Wiens 2010; Price et al. 2012; Rojas et al. 2012; Pyron and Wiens 2013; Title
and Burns 2015, Rolland and Salamin 2016), but none of them explicitly tested or
discussed whether effect-macroevolution or species selection was the main processes
driving diversification patterns.
Our main goal here is to develop a conceptual framework to disentangle between
effect-macroevolution and species selection through the identification of the biological
level at which natural selection is more important to determine diversification patterns. In
addition, our framework also aims to evaluate the existence of a potential conflict
between levels. We constructed our framework based on Lewontin’s triad – variability,
heritability and interaction – acting over an organism level trait as well as over a species-
94
level trait. We focus on the ecological niche as the biological trait under selection owing to
several studies which already discussed the association of this trait with clade dynamics
(see Title and Burns 2015). We first provide a brief overview of different interpretations
on ecological niche and then describe our working concept of ecological niche as an
aggregate trait that interacts with the environment. Later, we discuss how the conceptual
and methodological advances on niche evolutionary dynamics could be useful to
understand niche heritability. Finally, we build our conceptual framework under several
premises to provide a set of predictions that can help to identify effect-macroevolution or
species selection as the main evolutionary process behind diversification patterns.
Niche
One of the most intensively studied but yet controversial properties of species is
their niche (McInerny and Etienne 2012; Soberón 2014). Niche can be broadly defined as
an abstraction of the species’ relationship with the environmental conditions, but, despite
or perhaps because of its long history, there is still considerable debate over the meaning
of the term ‘niche’ (McInerny and Etienne 2012). Indeed, it is currently accepted that the
niche can be composed by different variables (e.g. ‘scenopoetic’ or ‘bionomic’; Hutchinson
1978; Soberón 2007), can have different “components” (e.g. fundamental or realized;
Hutchinson 1957), and can be described at different biological levels (e.g. organism or
species level; Bolnick et al. 2003; Myers and Saupe 2013).
George Evelyn Hutchinson formalized the niche concept as the set of scenopoetic
and bionomic variables that permit species to exist indefinitely (Hutchinson 1978).
Scenopoetic variables are composed by abiotic properties of the environment such as
95
temperature or precipitation, whereas bionomic variables are composed by different
types of resources such as preys, sexual mates or nest sites whose availability is associated
with biotic interactions like competition, mutualism, parasitism or predation (Hutchinson
1978, Soberón 2007). Moreover, he demonstrated through a set-theoretic representation
that two species that occupy similar areas in the geographical space have necessarily to
occupy different areas in the environmental space (Hutchinson 1957). In other words,
each species has their own set of environmental conditions in which it can exist
indefinitely: its fundamental niche. And, owing to negative biotic interactions, each
species occupies just a part of available environmental space: its realized niche. Another
important contribution of Hutchinson’s work was the recognition of an interface between
the geographical (G) and environmental (E) space (Colwell and Rangel 2009). The
geography-environment duality is asymmetrical because different regions in G-space
represent specific regions in E-space whereas the opposite is not necessarily true. That is,
there is a one-to-one relationship from G- to E-space but a one-to-many relationship from
E- to G-space (Soberón and Nakamura 2009). Besides theoretical advances in
understanding the interaction between both spaces, the geography-environment duality
has also had important implications in biogeography and macroecology. For instance, this
theoretical reasoning highlights that the geographical distribution of a species is ultimately
determined by three main aspects: the abiotic conditions defining its fundamental niche,
biotic factors defining its realized niche and the regions accessible to dispersal (see the
BAM diagram of Peterson and Soberón 2005; 2012).
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More recently, Soberón (2007) proposed the separation of the niche concept on the
basis of spatial scale. He proposed the distinction between Grinnellian and Eltonian
niches, with the first concerning broad-scale scenopoetic variables defining the conditions,
such as climatic variables, that a given species can occupy whereas the second referring to
bionomic variables representing resources at the local scale that a species can consume
(Soberón 2007). This separation allows disentangling local from regional processes, and
has direct implications in the growing literature that focus on species’ niches to answer
macroecological and biogeographical questions (Colwell and Rangel 2009; Peterson and
Soberón 2012).
Niche as an aggregate trait
All niche concepts discussed above are based on the idea of the niche being an
abstraction of a species’ relationship with its environment. Consequently, any attempt to
consider the niche within a conceptual framework of species properties being influenced
by natural selection, like ours, may suffer from circularity. This circularity may arise
because, on one hand, natural selection would act through the interaction of the
environment with the species’ trait, in this case its niche. But, on the other hand, niche is
already defined as the relationship of a species with its environment. Thus, to avoid this
potential issue, we explicitly consider the species’ niche as a biological trait that can be
inherited and whose interaction with the environment might provide differential fitness.
Under this view, niches are potentially subject to natural selection caused by the
environment as any other traditional biological trait.
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Is the niche an aggregate or an emergent “trait”? Niche is traditionally interpreted
as an aggregate trait, where species’ environmental requirements can be reduced to
organisms (Simpson 1944; Vrba 1987; Jablonski 2008). Currently, some authors interpret -
implicitly or explicitly - niche as a species-level, emergent trait (Losos 2008; Wiens et al.
2010; Myers and Saupe 2013), while others still maintain the traditional interpretation of
the niche as an organism level, aggregated trait (Bolnick et al. 2003; Araújo et al. 2011).
Such dichotomy is associated with the variables used to determine the species niche.
Authors favoring the niche as an aggregate trait focus on Eltonian niches, in which the
niche is defined, for example, as dietary items that organisms consume and can be used to
characterize organisms either as generalists or specialists (Bolnick et al. 2003). This
interpretation of the niche as an aggregate trait relies on Optimal Forage and Quantitative
genetic theory (Araújo et al. 2011). Alternatively, authors favoring the niche as an
emergent trait focus on Grinnellian niches, defining the niche as the set of abiotic
conditions that species are adapted to (Pyron and Wiens 2013, Rolland and Salamin 2016).
However, most of these authors do not explicitly equate Grinnellian niches with
emergent, species-level traits. An important exception is Myers and Saupe (2013), who
explicitly defined the Grinnelian niche as an emergent trait of species. For them, any
association that organisms have with abiotic conditions should be interpreted as
environmental tolerance of the species as a whole and not as an intrinsic organism trait
(Myers and Saupe 2013).
Here, we assume the niche – whether Eltonian or Grinnellian - as an aggregate trait
of the species. We believe that this consideration is the most operational for the
98
advancement of macroevolutionary theory. According to Jablonski (2007), an emergent
trait is a feature of a given biological level whose evolutionary consequences are not
affected by how the feature is generated at lower biological levels. However, as we are
going to elaborate in the final part of this paper, organism level niches can also affect
diversification patterns as well as the species-level niche. Consequently, we argue that
niche should be interpreted as an aggregate, rather than an emergent trait, and that its
variability can be quantified (first element of Lewontin’s triad).
Niche evolutionary dynamics and heritability
The second element of Lewontin’s triad for the occurrence of natural selection its
trait heritability. Traditionally, researches used simple correlation of a given trait - e.g.
range size - between ancestor-descendant species pairs to test for trait heritability
(Jablonski 1987; Webb and Gaston 2003). With the high advancement of phylogenetic
comparative methods (Harvey and Pagel 1991, Pennel and Harmon 2013), trait heritability
has now being tested within an explicit phylogenetic perspective and with more
sophisticated methods (Machac et al. 2011; Cardillo 2015).
Phylogenetic comparative methods were traditionally used to understand traits’
evolutionary dynamics - such as whether a trait is conserved or labile over time - rather
than heritability (Freckleton et al. 2002; Pennell and Harmon 2013). For example, to test
whether closely related species resemble each other more than expected by chance in
relation to their ecological attributes (i.e. niche conservatism; NC; Pearman et al. 2008),
authors have quantified the phylogenetic signal of species niches (Wiens et al. 2010). In
these studies, a statistically significant signal was interpreted as evidence for niche
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conservatism, whereas an absence of a signal was interpreted as the niche being a labile
trait. However, this analytical framework has important drawbacks. For instance, there is
no agreement as to what extent should be the level of signal to assume conservatism
(Losos 2008; Wiens 2008), the signal itself may be scale-dependent both in spatial and
temporal terms (Cavender-Bares et al. 2009), and might present phylogenetic non-
stationarity (Diniz-Filho et al. 2010; 2015). Finally, there is evidence that different
evolutionary processes could result in the same levels of phylogenetic signal (Revell et al.
2008).
Despite these drawbacks, we still consider phylogenetic comparative methods to be
very useful in testing for niche heritability (see Machac et al. 2011; Cardillo 2015).
However, it is necessary to define the ecological niche as a species’ property and then
interpret its phylogenetic signal as representing heritability instead of evolutionary
dynamics. Phylogenetic signal could represent heritability because, under a neutral
evolutionary model, such as Brownian motion, trait variability among lineages is linearly
correlated with time (Felsenstein 1985). The basic assumptions underlying this pattern are
a deterministic genetic component, which constrains trait variability, and a stochastic
component, such as genetic drift, which permits trait variability to increase proportionally
with time. Thus, the genetic component constraining trait variability could be interpreted
as "similarity by descendent", which in turn, can be a direct surrogate for heritability.
Others processes involving the selective process, such as a floating natural selection
through time mimetizing a random walk model, could also determine a phylogenetic
signal expected under Brownian motion (Revell et al. 2008). Nevertheless, these
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alternative processes does not invalidate the use of the signal as a surrogate of heritability
since heritability is also a basic assumption of natural selection (Lewontin 1970).
Conceptual framework
We have already argued how species niche could be understood as an aggregate
trait that possess variability, can be downscaled to the organismal level, and may present
heritability. Based on these conditions and assuming Lewontin's third premise - niche
interacts with the environment resulting in differential reproduction, we propose a
conceptual framework to evaluate whether effect-macroevolution or species selection
acting upon species niches is more important to mediate diversification patterns. First, we
define the system that we were interested to understand. Second, we establish which
property of the system was more important for testing and disentangling between causal
processes (effect-macroevolution or species selection). Third, we determine which causal
processes were the main drivers of the system’s property. Fourth, we identify the
premises of the potential causal processes. Fifth, we propose testable predictions. Finally,
we highlight how this conceptual framework could be important for future analyses to
understand which evolutionary processes are more important to explain diversification
patterns.
The system that we are interested to explain is the phylogenetic tree of a given
taxonomic group. The specific property of this system that we are interested in is the
diversification pattern, which represents the balance between speciation (λ) and
extinction (μ) rates. We assume natural selection as the general mechanism shaping the
phylogenetic tree and the ecological niche as the biological trait under selection
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The ecological niche is composed of the values of the environmental space that each
species and organism is adapted for. For simplicity, we assumed an one-dimensional
environmental space (E-space) which can be a variable representing a given niche variable
(i.e. scenopoetic or bionomic). Since niche is an aggregate trait, species as well as
organisms present niche properties (Figure 1). We considered two niche properties:
breadth and value (Quintero and Wiens 2013). Niche breadth is the set of environmental
values that each species and organisms are adapted to, whereas niche value is the
environmental value where each species and organism reaches its highest fitness. Thus,
there are three types of species in terms of niche breadth: generalist species composed by
generalist or specialist organisms (GEN-gen or GEN-spe, respectively), and specialist
species composed by specialist organisms (SPE). We did not assume specialist species with
generalist organisms (i.e. SPE-gen) because the organisms of such species would always be
specialist when compared to organisms of generalist species. In terms of niche value,
specialist species and organisms can establish a restricted niche value, whereas generalist
species and organisms tend to establish different niche values within their niche.
102
Figure 1. Environmental space with niche breadth and value of each species and organism. Two
types of species and organisms in terms of niche breadth: specialist or generalist. Note that each
specialist species occupy a certain niche value, and their organisms occupy the same niche value.
E-space means environmental space.
Since we assumed species niche as an aggregate trait, two evolutionary processes
could explain diversification patterns: effect-macroevolution or species selection. On the
one hand, if effect-macroevolution is the main process, the environment acts only upon
organisms' niche breadth resulting in differential fitness among organisms. Consequently,
this microevolutionary process is scaled-up to the species level - i.e. upward causation -
103
resulting in differential diversification. Thus, we assumed that if GEN-gen or SPE species
presents higher fitness than GEN-spe species, effect-macroevolution is the main process
driving diversification patterns. Because the former species present the same niche
breadth at both biological levels (species and organisms), whereas the latter species
present different niche breadths between species and its organisms. Therefore, it is more
parsimonious to infer effect-macroevolution rather than species selection as the main
causal process. On the other hand, if species selection were the main process, this would
necessarily generate a cross-level conflict between fitness associated with niche breadth.
Cross-level conflict occurs when a given niche breadth - e.g. specialist - at the organismal
level results in high organism fitness but a different niche breadth - e.g. generalist - at the
species level also results in high species fitness. Thus, we assume that if GEN-spe species
present higher fitness than GEN-gen or SPE species, species selection is the main causal
process driving diversification patterns. Since we assumed niche as an aggregate trait, the
absence of cross-level conflict means that only effect-macroevolution can be raised to
explain the diversification pattern.
Premises
To understand which macroevolutionary process is more important on shaping
diversification patterns, we assumed a spatially explicit model (Figure 2; see all the
premises in Table 1). Each geographic locality has a corresponding niche value (Birand et
al. 2012), thus each locality has a particular scenopoetic or bionomic value that organisms
as well as species are adapted for. At the organismal level, evolutionary fitness is
represented by reproduction and survival (Darwin 1859). We assumed panmictic species
104
(i.e. random mate across organisms); where specialist as well as generalist organisms have
the same probability to reproduce (Hubbel 2001). Probability to survive (hereafter,
fitness) at a given locality is determined by competition and niche value (Gascuel et al.
2015). We assume that specialist organisms of specialist species are more adapted to their
particular niche value than organisms of generalist species (Wilson and Yoshimura 1994,
Burin et al. 2016). Thus, for a given niche value where specialist organisms are adapted
for, they will always be better competitors, and, consequently, will present higher fitness
than generalist organisms. Others factors could also determine how well adapted an
organism is to a particular niche value, such as variation in physiological competences and
generation duration, but here, for the sake of simplicity, we only assume the degree of
specialization.
.
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Figure 2. Environmental space mapped into the geographic space. Environmental space is
represented by a continuous variable but we discretized it for the sake of simplicity. Colors: white
= low; gray = intermediate; black = high. E-space means environmental space and G-space means
geographic space
Table1. Premises to test predictions of both hypotheses: effect-macroevolution or species
selection.
Features Premises References
Environmental
space (E-space)
Represented by scenopoetic and/or bionomic variables;
Considered as a one-dimensional space.
Hutchinson (1978).
Birand et al. (2012).
106
Niche Organismal and species trait (i.e. aggregate trait);
Heritable at both organismal and species level;
Represents the breadth and value that each species and organism
occupies in the environmental space.
Vrba (1987).
Quintero and Wiens
(2013).
Geographic
Space
Spatial representation of the environmental space.
Each geographic locality represents one value in environmental
space.
Hutchinson (1957).
Birand et al. (2012).
Species and
organisms
Three types of species and their organisms in terms
of niche breadth:Generalist species with generalist organisms
(GEN-gen)
Generalist species with specialist organisms (GEN-spe)
Specialist species (SPE)
Organism level
processes
Three processes: reproduction, survival and migration;
Reproduction is independent of niche;
Fitness is assumed as survival;
Survival is dependent on competition and niche value;
For a given niche value, specialist organisms will
present higher fitness than generalist organisms;
Species fitness is modeled by a normal function;
Migration is independent of niche;
Probability to migrate between localities is modeled
by an exponential function.
Hubbel (2001).
Gascuel et al. (2015).
Wilson and
Yoshimura (1994).
Hubbel (2001).
Hubbel (2001).
Species-level
processes
Two processes: speciation and extinction;
Speciation is dependent on distance and time of isolation between
Jablonski (2008).
Mayr (1963);
107
populations and niche value of the locality where each population
occurs;
Extinction is dependent on geographical distribution and
population size.
Gascuel et al. (2015).
Ceballos and Erlich
(2002); Reed (2005).
Effect-
macroevolution
GEN-gen and SPE species present higher diversification.
Species selection GEN-spe species presents higher diversification.
To model both factors – competition and niche value – determining organism
fitness, we assumed a normal fitness distribution of niche value for each type of species
(Figure 3). For specialist species, we assumed a normal distribution with a small standard
deviation representing its specialization to a particular niche value (Figure 3a). For
generalist species, we assumed a normal distribution with larger standard deviation than
for specialist species, but with a lower fitness peak (Wilson and Yoshimura 1994; Figures
3b and 3c). Each type of organism also has its own normal fitness distribution, where
specialist organisms have distributions with standard deviations similar to specialist
species and generalist organisms have distributions with standard deviations similar to
generalist species. Specialist organisms of specialist species will have higher fitness for the
niche value where they are adapted for than organisms of generalist species (Wilson and
Yoshimura 1994).
108
Figure 3. Fitness distributions of niche value for three types of species. Species types are based on
niche breadth: specialist species with specialist organisms (SPE), generalist species with specialist
organisms (GEN-spe) and generalist species with generalist organisms (GEN-gen). Thick lines
represent species distributions, whereas dotted lines represent distributions for organisms. Note
that specialist species will have higher fitness than generalist species for the niche value where
they are adapted for.
The probability of organisms to disperse across geographic localities is independent
of their niche characteristics (Hubbel 2001). Thus, we assumed that the probability to
disperse is dependent on the distance between the localities where the organism occurs
to the locality where the organism will disperse to ("Isolation by distance" effect, Wright
1943). Therefore, the dispersion probability can be represented as an inverse exponential
function of distance (Hubbel 2001).
At the species level, evolutionary fitness is represented by speciation and/or
extinction (Jablonski 2008). We assumed the speciation events occurring in allopatry
109
(Mayr 1963, Barraclough and Vogler 2000). Speciation is dependent on three main factors:
distance between populations, time of isolation and niche value (Mayr 1963, Gascuel et al.
2015). There is a minimum distance between populations where the probability to
exchange organisms is so low that they can be considered isolated populations. Such
probability of exchanging organisms between populations is determined by the
exponential function aforementioned (Hubbel 2001). Speciation is also affected by the
time that both populations have been isolated. In addition, populations may experience
different selective regimes depending on the environment present at the geographic
localities that they occupy. This environment is expressed by the niche value of each
geographic locality (Gascuel et al. 2015, Figure 2).
Two interrelated processes determine probability of extinction: geographical
distribution and local population size (Ceballos and Erlich 2002; Reed 2005). Geographical
distribution size represents the number of localities that the organisms of a given species
occupy and local population size is the number of organisms at a particular geographic
locality. Each local population has a minimum size or threshold at which stochastic
processes - being demographic, environmental or genetic - or inbreeding depression do
not affect its persistence for a short time period (i.e. minimum viable population; Reed
2003). Thus, for a given species to go extinct, a gradual reduction of its geographical
distribution is required until its last local population passes this threshold.
Predictions
Based on the multi-level hierarchical processes assumed as premises above, we
derive several predictions of speciation for GEN-gen, GEN-spe and SPE species (Table 2).
110
First, we could expect that GEN-gen and GEN-spe species will have higher probability of
speciation than SPE species (Gómez-Rodríguez et al. 2015). This would result because
generalist species have more localities with suitable environmental conditions and/or
biotic interactions than specialist species, resulting in larger geographic distributions
(Slatyer et al. 2013). However, because populations of generalist species are evolutionary
less fitted to a specific locality than populations of specialist species (Wilson and
Yoshimura 1994, Figure 3), thus more prone to local extinction, this might result on more
isolated populations and consequently more speciation events. There are empirical
evidences for this prediction for different groups such as amphibians (Gómez-Rodríguez et
al. 2015) and vascular plants (Ozinga et al. 2013). Second, we could expect that SPE
species will have higher probability of speciation than GEN-gen and GEN-spe species
(Rolland and Salamin 2016, Burin et al. 2016). This would result because: i) populations of
specialist species can colonize peripheral localities besides the fact this will happen with
low probability given that the dispersal process is modeled by an exponential function
(Hubbel 2001); ii) populations of specialist species will be evolutionary more fitted for
those peripheral localities than populations of generalist species (Wilson and Yoshimura
1994, Figure 3); and iii) peripheral populations are more likely to be isolated because the
dispersal process is modeled by an exponential function, where distant localities have
lesser probability of sharing organisms than nearby localities ("Isolation by distance"
effect, Wright 1943), and because they have narrower niches. As for the first prediction,
there are also empirical evidences for this prediction for several vertebrate groups such as
birds and mammals (Rolland and Salamin 2016, Burin et al. 2016).
111
Table 2 Predictions for speciation and extinction for each type of species based on their niche
breadth. Species: GEN-gen = generalist species with generalist organisms; GEN-spe = generalist
species with specialist organisms; SPE = specialist species.
Predictions Causes
Speciation
GEN-gen and
GEN-spe > SPE
Generalist species have more localities with suitable niches,
consequently, higher geographical ranges. Thus their populations
are more likely to be isolated.
GEN-gen and
GEN-spe < SPE
Specialist species are more prone to present isolated populations
because they have narrower niches, and, once a peripheral locality is
colonized, there is a high probability of its population being isolated
from the others.
Extinction
GEN-gen >
GEN-spe > SPE
Competition is more important than niche breadth. Consequently,
specialist species are better competitors within a given niche value
than generalist species. Generalist species with generalist organisms
have more availability of localities with suitable niches than
specialist organisms.
SPE > GEN-
gen and GEN-
spe
Niche breadth is more important than competition. Consequently,
generalist species have more localities with suitable niches, higher
geographic ranges, and number of populations.
GEN-gen =
GEN-spe = SPE
Migration and reproduction are more important than competition
and niche value (at each locality).
112
Following the same premises, we also derive several predictions of extinction for
GEN-gen, GEN-spe and SPE species. First, we could expect that SPE species would have
lower probability of extinction than GEN-gen and GEN-spe species (Rolland and Salamin
2016, Burin et al. 2016). This would result from specialist organisms of specialist species
being better competitors than organisms of generalist species within a given locality, since
the former organisms are better adapted to the available environmental conditions
and/or biotic interactions (Wilson and Yoshimura 1994). Rolland and Salamin et al. (2016)
showed that specialists are lesser prone to extinction than generalists for almost all
amphibians, birds and mammals. Moreover, we also expect that GEN-gen species would
have lower probability of extinction than GEN-spe species. This could happen because
even though generalist organisms will be evolutionary less fitted to a particular locality
than specialist organisms (Wilson and Yoshimura 1994), they will have the ability to
occupy other localities to maintain viable populations (Figure 3). A capacity that is not
presented by specialist organisms of either generalist or specialist species. Our second
prediction is that GEN-gen and GEN-spe species would have lower probability of extinction
than SPE (Gómez-Rodríguez et al. 2015). This would result from generalist species having
larger geographical distributions owing to their broader niches, and, consequently, higher
number of populations (Slatyer et al. 2013). For instance, Thuiller et al. (2005) showed
that European plants with narrower niches present lesser probability of extinction than
113
plants with wider niches. Third, we could expect that all three types of species will have
the same probability of extinction (Birand et al. 2012). This would result from the
interaction between migration and reproduction, which are niche-independent processes,
overcoming the effects of competition and niche value at each geographic locality. We
found no empirical but theoretical evidence from simulation models for this prediction
(Birand et al. 2012).
Assuming the balance between speciation and extinction, we should test these
predictions to verify whether effect-macroevolution or species selection is the main causal
process shaping diversification patterns. According to our premises and predictions, if
GEN-gen or SPE species present higher accumulation of species, then effect-
macroevolution can be considered the main causal process behind diversification given
that the trait of interest is present at the organism level (Vrba and Eldredge 1984).
Otherwise, if GEN-spe species present higher accumulation of species, then species
selection would be considered the main causal process given that the trait of interest is
present at the species level, and is different from the one present at the organism level,
thus causing a cross-level conflict (Diniz-Filho 2004, Jablonski 2008).
Moving forward
We consider our conceptual framework as a first formal attempt towards
disentangling the macroevolutionary consequences of effect-macroevolution and species
selection. Indeed, our framework can guide future analyses explicitly aimed at evaluating
whether effect macroevolution or species selection is more important to explain
diversification patterns. To test our proposed predictions, we advocate the necessity to
114
produce mechanistic models that, if possible, incorporate all aforementioned multi-level
processes and be oriented by observed patterns (Grimm and Railsback 2005). A
potentially fruitful research avenue is the development of individual-based models, where
simulating the interaction of individuals at multiple levels can help understand the main
processes shaping the properties of higher-level patterns (DeAngelis and Mooij 2005;
Grimm and Railsback 2005). Moreover, we also advocate that after answering the main
question posed by our framework (effect-macroevolution vs. species selection), other
questions should be addressed. Among others, some relevant questions can be the
following: which causal processes are more important in a scenario with temporal
variation in environmental conditions (see Gascuel et al. 2015)? What is the effect of
neutral process - such as genetic drift, as the basis of broad scale neutral dynamics – in
diversification patterns (see Rosindell et al. 2015, Chevin 2016)?
Concluding remarks
Recently, several studies have highlighted the potential association between
biological traits and diversification patterns. However, most of these studies are silent on
how processes occurring at different biological levels could affect these patterns. Here, we
have proposed a hierarchical conceptual framework to evaluate such multi-level processes
and test for effect-macroevolution and species selection driving macroevolutionary
patterns. We considered the ecological niche as an appropriate biological trait that can
undergo natural selection and highlighted the importance to define niche as an aggregate
trait to help disentangle between macroevolutionary processes. Finally, we believe that
115
more mechanistic-based models can be a possible solution to understand the hierarchical
nature of evolution.
Acknowledgments
We are indebted to Thiago F. Rangel and Tiago B. Quental for thorough discussions and
suggestions. FV thanks Mark E. Olson for introducing him to macroevolutionary theory
and for endless discussions on theory and science. DMCCA was supported by a
"Coordenação de Aperfeiçoamento de Pessoal de Nível Superior" (CAPES) doctoral
fellowship. FV was supported by a "Conselho Nacional de Desenvolvimento Científico e
Tecnológico" (CNPq) Science-without-borders grant (BJT 301540/ 2014-4). JAFDF is
continuously supported by a "Conselho Nacional de Desenvolvimento Científico e
Tecnológico" (CNPq) productivity fellowship.
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Capítulo 4
Bat species diversity dynamics through deep time
Davi Mello Cunha Crescente Alves1, Jesús N. Pinto-Ledezma1, José Alexandre Felizola
Diniz-Filho2and Fabricio Villalobos2,3
1Programa de Pós-Graduação em Ecologia e Evolução, Universidade Federal de Goiás,
CEP 74.001-970, Goiânia, Goiás, Brasil.
2Departamento de Ecologia, Universidade Federal de Goiás, CEP 74.001-970, Goiânia,
Goiás, Brasil.
3Red de Biología Evolutiva, Instituto de Ecología, A.C., CarreteraAntigua a Coatepec 351,
El Haya, 91070 Xalapa, Veracruz, Mexico.
126
Abstract
The species diversity dynamics of megadiverse clades over deep time is better explained
by the direct effects of large scale-environmental events, such as climate changes, sea-
level variations or mountains uplift, or by the competition between lineages for available
niches? Here we used several likelihood-based diversification models on bat's
megaphylogenies to explicitly evaluate support to these two hypotheses and also estimate
bat's diversification patterns through time. These models might assume constant
diversification rates through time or their diversification rates might vary through time
and be dependent of large-scale environmental processes or clade's diversity at different
periods - which represents lineage competition for available niches. We found that
diversity-dependent diversification models fitted better to bat's phylogenies than
environmental-dependent diversification models. This suggest that bat's diversity
dynamics through the Cenozoic were more determined by the Niche Availability
hypothesis than by the Environmental Change hypothesis. Moreover, we also showed
that, according to the diversification models tested, bat's diversity is still expanding and is
very far from its carrying capacity.
Key words: Adaptive radiations - Diversification rates - Ecological limits - Ecological
opportunity - Phylogenetic comparative methods - Phylogenetic uncertainty
127
Introduction
One important question in macroevolution is why biodiversity varied through deep time.
Any study aiming to answer this question should to consider speciation and extinction
rates as well as the balance between both rates, which gives the diversification rate
(Ricklefs 2007, Pyron and Burbrink 2013). These macroevolutionary rates can now be
directly estimated from molecular phylogenies using many recently developed methods
(Nee et al. 1994, Morlon 2014). Despite the fact these phylogenies are constrained by
complete and accurately time-calibrated trees, these informations have constantly been
improved with the availability of megaphylogenies, at least for some vertebrate clades
such as amphibians (Pyron and Wiens 2011), birds (Jetz et al. 2012) and mammals
(Bininda-Emonds et al. 2007). Moreover, it is important to highlight the ever increasing
development of sophisticated phylogenetic comparative methods that can estimate
diversification parameters more accurately and incorporate time-varying rates (Morlon et
al. 2011, Stadler 2011).
Despite recent advances in phylogenetic data availability and phylogenetic methods
to handle such data, diversification rate is only a proxy for one or more causal
mechanisms affecting the diversity dynamics of a given clade over deep time (Stadler
2013). Thus, it is necessary to use statistical models that explicitly incorporate such causal
mechanisms influencing diversification rates and, consequently, allowing to discriminate
between different macroevolutionary hypotheses to fully understand this temporal
diversity dynamics of a particular clade. Altough several hypotheses have been proposed
(Table 1), only two present an explicit causality for diversity dynamics: the Environmental
Change hypothesis (Barnosky 2001) and the Niche Availability hypothesis (Schluter2000).
Table 1. Macroevolutionary hypotheses for diversity dynamics through deep time. Also, their
causality, description, prediction and references. Notice that only the Environmental Change and
Niche Availability hypotheses presents an explicit causality for diversity dynamics. References are
related to some works which proposed mathematical models to test for the given hypothesis.
128
Hypotheses Causality Description Prediction References
Null 1 None No causal factor
affects speciation
dynamics through
deep time; no
extinction events.
Constant speciation
rate through time.
Yule (1925)
and Morlon
et al.
(2016).
Null 2 None No causal factor
affects
diversification
dynamics through
deep time.
Constant speciation
and extinction rates
through time.
Raup et al.
(1973), Nee
et al. (1994)
and Morlon
et al.
(2016).
Time* None Time is a proxy of
some causal factor
not explicitly
modeled which
affects
diversification
dynamics through
deep time.
Speciation and/or
extinction rates
varies through time.
Nee et al.
(1994),
Rabosky
(2006) and
Morlon et
al. (2011)
Environmental
Change
Climate
Change
(temperature)
Climatic events
through deep time
directly affect
diversification
dynamics.
Speciation and/or
extinction rates are
correlated with
global mean
paleotemperatures
through time.
Condamine
et al. (2013)
and Morlon
et al.
(2016).
Environmental
Change
Sea-level The variation in
sea-level through
deep time, which
consequently
affects the
availability of
Speciation and/or
extinction rates are
correlated with sea
level variation
through time.
Condamine
et al. (2017)
and Morlon
et al.
(2016).
129
terrestrial area,
affects
diversification
dynamics.
EnvironmentalChange Andean Uplift The uplift of the
Andes during the
Cenozoic, which
created dispersal
barriers and also a
large
environmental
heterogeneity
gradient in the
most species rich
region of the world
(i.e. Northwest
Amazon), affects
diversification
dynamics.
Speciation and/or
extinction rates are
correlated with
altitudinal variation
of the Andes
through time.
Condamine
et al. (2017)
and Morlon
et al.
(2016).
Niche Availability Intra-clade
Competition
The occupation of
a new ecological
niche is responsible
for ecological
speciation, thus,
because niche is
limited, its
availability affects
diversification
dynamics through
deep time.
Speciation and/or
extinction rates are
correlated with the
number of lineages
of the clade through
time.
Rabosky
and Lovette
(2008) and
Etienne et
al. (2012).
*Not confound with the hypothesis used to explain diversity differences between clades or
regions, which is based on comparing divergence times between clades or colonization of regions.
130
In short, the Environmental Change hypothesis postulates that temporal changes on
the abiotic environment directly affect diversification rates and are thus responsible for
diversity dynamics (Benton 2009, Condamine et al. 2013). For instance, increases in global
mean paleotemperatures might trigger diversification dynamics through accelerating
biological rates at different biological levels; i.e. from accelerating nucleotides substitution
at the molecular level to shortening generation time at the population level and, thus,
increasing speciation rates at the clade level (Rohde 1992, Allen et al. 2007). Alternatively,
decreases in global mean paleotemperatures might reduce the availability of
environmentally suitable areas that could then trigger an increase of extinction events
(Mannion et al. 2013). Other environmental changes potentially responsible for
diversification dynamics might be global variations on sea-levels, which directly affect the
availability of geographic areas (Miller et al. 2005), or the uplift of major mountain chains
in high species rich regions, such as the Andes in the Neotropics, which directly or
indirectly create dispersal barriers and steep environmental gradients for lineages (Moen
and Morlon 2014, Condamine et al. 2017). Accordingly, the main prediction of these
environmental-based hypotheses is that diversification rates are directly linked to the
temporal variation of the environmental setting encountered bylineages (Condamine et al.
2013).
131
Figure 1. Examples of causal factors that could affect diversification dynamics through deep time.
Diversification rates could be directly affected by large-scale environmental processes, such as
global paleotemperatures through the Cenozoic, or by the number of lineages of its own clade at
each time interval, which represents lineage competition for available niches. Both curves are
hypothetical.
Conversely, the Niche Availability hypothesis postulates that the colonization of a
new niche results in ecological speciation and, because the availability of these niches is
limited, the competition for niche space can thus regulate the diversification dynamics of
a clade (Schluter 2000). Such diversification dynamics under niche availability results in an
initial explosive radiation in the clade's history owing to the colonization of empty niches
by ancestral lineages and followed by a diversification slowdown as available niches get
saturated (Rabosky 2009). The availability of a new niche might be determined by: i) the
extinction of a competitor and/or predator, ii) the dispersal to a new region, iii)
environmental changes on the original region, or iv) the acquisition of a key innovation
(Etienne and Haegeman 2012). Thus, a particular prediction of this hypothesis is that a
clade’s diversification dynamics is directly linked to the number of lineages that such clade
132
presents at particular periods of time (i.e. diversity-dependence), which in turn implies
lineage competition (Figure 1; Rabosky and Lovette 2008, Etienne et al. 2012).
To the extent of our knowledge, we are aware of only few studies that have used
environmental and diversity-dependent diversification models to simultaneously test both
macroevolutionary hypothesesto understand diversity dynamics. So far, most studies have
only tested the null hypothesis that diversification is constant through time (Morlon et al.
2011, Stadler 2011, Shi and Rabosky 2015) or tested this null hypothesis against one of the
two aforementioned alternative hypotheses (Rabosky and Lovette 2008, Yu et al. 2014).
One exception was Etienne et al. (2012), whotested a diversity-dependent against an
environmental-dependent model to determine temporal variation on Cetacean
diversification. They found that the restructuring of the oceans was more important than
lineage competition for ecological niches to explain Cetacean diversity dynamics over the
last ~36 million years.
The Order Chiroptera is a very suited clade to test the relative importance of both
macroevolutionary hypotheses in explaining diversity dynamics of megadiverse clades
through deep time. Bats have a high current diversity, with ca. 1300 species, and present
an evolutionary history that encompasses almost all major Cenozoic environmental events
(Teeling et al. 2005, Shi and Rabosky 2015). Moreover, there is no consensus on whether
bats diversity dynamics has been more determined by the effect of large-scale
environmental changes or by lineage competition for available niches. For instance,
several studies detected an early burst on bats diversification with a subsequent
slowdowns throughout their evolutionary history (Figure 2; Jones et al. 2005, Yu et al.
2014, Shi and Rabosky 2015). This diversification pattern is traditionally expected under
the Niche Availability hypothesis (Phillimore and Price 2008, Morlon et al. 2010), where,
specifically for bats, may have been caused by the increase of plants and insects
diversification rates during the Early Eocene, ca. 50 million years ago (Wilf and Labandeira
1999). Because plant and insect clades are important ecological resources for bats, their
increased diversification may have been also related to an increase of bats diversification
with a subsequent decrease and stabilization with time (Jones et al. 2005, Teeling et al.
133
2005, Yu et al. 2014). However, this diversification slowdown might also be caused by the
direct effects of large-scale environmental changes such as climatic events and/or the
uplift of mountain ranges, as expected bu the Environmental Change hypothesis (Shi and
Rabosky 2015). Considering these alternative possibilities, there is a necessity to use an
analytical framework to explicitly discriminate between these
macroevolutionaryhypotheses to explain the diversity dynamics of bats through deep
time.
Figure 2. Lineage through time plot for bats. This plot is based on the supertree provided by
Jones et al. (2005) and shows that bat's diversification is slowing down. The x-axis is from the past
to the present.
Here, we take advantage of a recent analytical pipeline to evaluate and tease apart
the relative importance of the Environmental Change and Niche Availability hypotheses in
explaining the bat diversity dynamics over deep time. This analytical pipeline contains
several diversification models that explicitly incorporate both causal factorsand also
134
estimate bats speciation and extinction rates through time. We also evaluated the effect
of phylogenetic uncertainty into our analyses by fitting the models using two alternative
phylogenies with distinct completeness and branch length estimates.
Methods
Data
To evaluate which macroevolutionary hypothesis better explained bats diversity
dynamics through deep time, we used the two most updated and comprehensive time-
calibrated species-level phylogenies available for all bats (Jones et al. 2005, Shi and
Raboski 2015). The first phylogeny is the supertree provided by Jones et al. (2005) and
Bininda-Emonds et al. (2007), which was updated by Fritz et al. (2009; hereafter "Jones'
phylogeny"). This bats supertree, whose authors used fossil dates to estimate divergence
times of bat lineages, is based on several sub-clade molecular phylogenies and contains
81.1% of all extant bat species (1054 species). Because this phylogeny contains several
polytomies, we used the Maximum Clade Credibility supertree obtained from the
pseudoposterior distribution of dichotomicsupertrees provided by Kuhn et al. (2011) to
establish a fully resolved tree for the analyses. The second phylogeny used was the
maximum likelihood molecular phylogeny provided by Shi and Rabosky (2015) based on
mitochondrial and nuclear sequences of 29 loci (hereafter "Shi's phylogeny"). "Shi's
phylogeny" contains 62.5% of all extant bat species (812 species) and their authors also
used fossil dates to estimate divergence times of bat lineages. These phylogenies present
different crown ages with “Jone’s phylogeny” with ca. 72 million years ago and “Shi’s
phylogeny” with ca. 58 million years ago.
The other types of data used here were the three environmental variables needed
to test for the environmental hypotheses. These variables were: global mean temperature
(Zachos et al. 2008), global mean sea-level (Miller et al. 2005) and the maximum altitude
of the Andes mountain chains (Condamine et al. 2017). All these variables encompassed at
least all the Cenozoic era (~66 - 0 million years ago).
135
Diversification models
We used a recent analytical pipeline (Condamine et al. 2017) that contains 38
diversification models to represent five macroevolutionary hypotheses that can
potentially explain bats diversity dynamic through deep time (Table 1, Appendix3). Note
that only two of these hypotheses - Environmental Change and Niche Availability - has an
explicit causality, whereas the others (Null 1-2 and Time) does not present. All of the
diversification models are based on the pioneering work of Nee et al. (1994), who derived
a likelihood function to estimate constant and time-varying speciation and extinction rates
directly from reconstructed phylogenies, such as molecular phylogenies. Morlon et al.
(2011) made some modification on their model and produced a time-dependent
diversification model which calculates the probability of observing a
reconstructedphylogeny at each cladogenetic event conditioned by the probabilities of
survival of the extant lineages that are descendant and not descendant from that
cladogenetic event. These survival probabilities are calculated from the balance between
speciation and extinction rates estimated at different time intervals. All the diversification
models used here allows the inclusion of phylogenies that present only a proportion of all
extant species, such as both bat's phylogenies used here (Morlon et al. 2016, Etienne et al
2012).
Constant models
To represent the Null hypotheses of stochastic diversification, we used the constant
speciation model (Yule 1925; Null 1) and the constant speciation and extinction model
(Raup et al. 1973, Nee et al. 1994; Null 2). The constant-speciation model assumes that
bats macroevolutionary history presented no extinction event, whereas both of these
models assume no causality to explain bats speciation and extinction events and that
these events are constant through time.
Time-dependent models
136
To represent the Time hypothesis, we used a set of 8 time-dependent
diversification models (Morlon et al. 2011, Morlon et al. 2016). All these models, as
explained above, assume that speciation and/or extinction might vary through time. Their
particularities are based on their premises about the studied clade’s
macroevolutionaryhistory: presence or absence of extinction events, whether speciation
or extinction rates are constant through time, and whether the function representing the
association of speciation and/or extinction with time is linear or exponential. Despite
"time" is not a direct causal factor regulating diversification rates, we decided to use time-
dependent diversification models because "time" could represent other causal factors not
included on the models below.
Environmental-dependent models
To represent the 3 environmental hypotheses - Climate change, Sea-level and
Andean uplift, we used a total of 24 environmental-dependent diversification models; i.e.
a set of 8 models for each hypothesis (Condamine et al. 2013, Condamine et al. 2017). All
these models explicitly assume that the variation of speciation and/or extinctions rates
through time is directly dependent on a given environmental variable: global mean
temperature, global mean sea-level or the maximum altitude of the Andes mountains
chain. Thus, these environmental-dependent models are basically a transformation of the
aforementioned time-dependent diversification models proposed by Morlon et al. (2011).
The environmental effect is incorporated in the time-dependent models by estimating at
each cladogenetic event the regression coefficient for the relationship between speciation
and/or extinction with the environmental variables (Condamine et al. 2013), whereas this
relationship might be linear or exponential. The particularities of each environmental-
dependent diversification model are similar to those in time-dependent models: presence
or absence of extinction events, whether speciation or extinction rates are constant
through time, and whether the function representing the association of speciation and/or
extinction with a specific environmental variable is linear or exponential (Condamine et al.
2013).
137
Diversity-dependent models
Finally, to represent the Niche availability hypothesis, we used a set of 4 diversity-
dependent diversification models that are a direct modification of the constant speciation
and extinction model from Nee et al. (1994; and not from Morlon et al. 2011). These
diversity-dependent models explicitly assume that speciation and/or extinctions rates are
directly influenced by the number of lineages that the clade presents at each time
interval. They also assume thatclade has reached its carrying capacity when the number of
lineages has occupied all available niches, and, consequently, the clade reaches its
diversity equilibrium with speciation rates equaling the extinction rates (Etienne and
Haegeman 2012, Etienne et al. 2016). Becauseextinct lineages and the non-sampled
extant lineages also contribute to this diversity-dependence, Etienne et al. (2012) used a
Hidden Markov Model to compute the likelihood of speciation and extinction rates given
the reconstructed phylogeny as well as all extinct lineages and non-sampled extant
lineages not included on this reconstructed phylogeny. The particularities of these
diversity-dependent models were: i) an exponential relationship between speciation
events with clade's diversity through time and constant extinction rate through time, ii) a
linear relationship between speciation events with clade's diversity through time and no
extinction events, iii)a linear relationship between speciation events with clade's diversity
through time and constant extinction rate through time, and iv) a linear relationship
between speciation and extinction events with clade's diversity through time.
Model selection
We fitted all 38 diversification models based on "Jones' phylogeny" and on "Shi's
phylogeny" to account for phylogenetic uncertainty. We used the sample-size corrected
Akaike Information Criterion (AICc) to select the best-fitting model given each bat's
phylogeny, which, consequently, allowed us to select the best macroevolutionary
hypothesis to explain bats diversity dynamic through deep time considering phylogenetic
uncertainty. Then, we used the AIC weights (AICw) of each model to estimate weight-
averaged speciation and extinction rates (Burnham and Anderson 2002).
138
All analyzes were performed in the R environment (R Development Core Team,
2016), using the packages RPANDA (Morlon et al. 2016) for the constant diversification,
time-dependent and environmental-dependent diversification models, the package DDD
(Etienne et al. 2012, Etienne et al. 2016) for the diversity-dependent diversification
models, andpackage "MuMIn" (Bartón 2016) for AICw.
Results
The macroevolutionary hypothesis that best explained bats diversity dynamics
through deep time was the Niche Availability hypothesis (table 2). This result was
consistent for both phylogenies considered and for which a diversity-dependent
diversification model was significantly better fitted than the diversification models for all
the other hypotheses (see Appendix3 for details of parameters and model selection for all
diversification models). For the "Jones’ phylogeny", the best-fitted diversity-dependent
model assumed a linear relationship between speciation and extinction rates with bat's
diversity through time (AICw = 1; Table 2), whereas for the "Shi's phylogeny", the best-fit
diversity-dependent model assumed a linear relationship between speciation withbat's
diversity through time and constant extinction rates (Appendix3).
Table 2. Selection of the best diversification models representing each macroevolutionary
hypotheses for bat's diversity dynamics through deep time. Each macroevolutionary hypothesis
presents different models (except Null 1 and 2; see Appendix3) based on their parameters
(speciation and/or extinction) and the function (linear or exponential) between
speciation/extinction and its causal factor. These results are based on "Jones' phylogeny". AICc =
sample-size corrected Akaike Information Criterion, ΔAIC = delta Akaike Information Criterion and
AICw = weight Akaike Information Criterion.
Hypotheses Causality Models Function AICc ΔAIC AICw
Null 1 Constant speciation - 6746.92 2571.34 0
139
Null 2 Constant
speciation/extinction
- 6744.53 2568.95 0
Time Time-dependent
speciation/extinction
Linear 6703.06 2527.48 0
Environme
ntal
Climate
change
(temperature)
Environment-
dependent
speciation/extinction
Linear 6712.25 2536.66 0
Environme
ntal
Sea-level Environment-
dependent
speciation/extinction
Linear 6720.4 2544.82 0
Environme
ntal
Andean Uplift Constant speciation
/environmental-
dependent extinction
Linear 6720.38 2544.8 0
Niche
Availability
Diversity-dependent
speciation/extinction
Linear 4175.58 0 1
Bats diversity showed a pattern of increase through time (Table 3). For "Jones'
phylogeny", bats net diversification rate was 0.001 lineages per million years with the
clade reaching an "equilibrium" with more than 20000 bats. Now, for "Shi's phylogeny",
bats net diversification rate was 0.08 lineages per million years with the clade reaching an
"equilibrium" with almost 8000 bats. Note that because only one diversity-dependent
diversification model had an AICw =1 for each phylogeny, we actually used only its results
for estimating diversification rates for each phylogeny.
Table 3. Speciation and extinction rates determining bats diversity dynamics through deep
time. The best model was the diversity-dependent diversification model of the Niche availability
hypothesis for both phylogenies. r = net diversification rate; K = the number of lineages where the
clade reaches an "equilibrium state".
140
Phylogeny Model Speciation Extinction r K
Jones et al.
(2005)
Linear diversity-
dependent
speciation/extinction
0.5 0.499 0.001 20304.11
Shi and
Rabosky
(2015)
Linear diversity-
dependent speciation
and constant
extinction
0.413 0.333 0.08 7958.54
Discussion
Several macroevolutionary hypotheses have been proposed to explain diversity dynamics
of megadiverse clades through deep time (Table 1), yet no consensus has been reached on
which hypothesis best explains such dynamics (Benton 2009). Our results for bats suggest
that the Niche Availability hypothesis presents the best explanation for this clade’s
diversity dynamics, even after accounting for phylogenetic uncertainty. Moreover, our
results indicate that bats diversity seems to be increasing over time and is very far from
reaching its carrying capacity, according to the evaluated models.
The Niche Availability hypothesis is the best explanation for bats diversity dynamics
through deep time (Table 2). Our diversity-dependent diversification models fit bats
macroevolutionary history considerably better than the other models evaluated, such as
the environmental ones.This indicates that lineage competition for ecological niches was
more important for the diversification of bat lineages than the direct effect of
environmental events throughout the Cenozoic, such as climate changes or mountain
uplift. This result supports the view of different authors who suggested that the
discernable early burst-slowdown dynamic on bats diversification through time was
caused by the rise of global temperatures during the Early Eocene Climatic Optimum. This
climatic event provided a great availability of ecological niches for bats, on their early
141
history, with the rise of plants and insects diversities (Jones et al. 2005, Teeling et al. 2005,
Yu et al. 2005). Notice that this mechanism is only an indirect effect of a large-scale
environmental event and should not be confounded, for instance, with direct temperature
effects upon bats diversification as expected under the Environmental Change hypothesis.
The evidence we found for the Niche Availability hypothesis was not affected by
phylogenetic uncertainty. Besides the fact that both considered phylogenies have
different crown ages and proportions of non-sampled extant species, they were clearly
better fit by diversity-dependent models compared to the other diversification models
(Appendix 3). The considerable differences provided by both phylogenies were related to
whether extinction was constant through time (Table 3), the estimation of extinction rates
(Appendix 3) and the estimation of clade's carrying capacity (Table 3). The best-fitted
model supported by "Jones' phylogeny" presented a linear relationship between
extinction and bat's diversity dynamics, whereas the best-fitted model supported by "Shi's
phylogeny" presented a constant extinction rate through time (Table 3). Moreover, the
majority of the 38 diversification models fitted to "Shi's phylogeny" presented very low
values for extinction rates (Appendix 3). We believe that this extinction results related to
"Shi's phylogeny" might be caused by the proportion of sampled extant species (62.5%),
which was considerably lower than the proportion of "Jones' phylogeny" (81.1%). Now,
we do not have a plausible explanation for the difference in the carrying capacity
suggested by both phylogenies.Thus, despite our support for the Niche Availability
hypothesis, further investigations are still needed to provide more precise parameter
estimates.
Bats as a clade still seem to be expanding and far from reaching an equilibrium state
of diversity (Table 3). Our results showed positive net diversification rates with a carrying
capacity much far from the actual number of extant bat species. Several studies have
suggested that the appearance of key innovations, such as flight capabilities and
echolocation, associated with the increase on plants and insects diversities in the Early
Eocene, triggered an explosive radiation at the dawn of bat's evolutionary history followed
by a subsequent diversification slowdown (Jones et al. 2005, Teeling et al. 2005, Yu et al.
142
2014). Besides the fact this diversification slowdown seems a pervasive pattern for bats
(Shi and Rabosky 2015) and expected under the Niche Availability hypothesis, our results
suggest that bat's diversification has not yet reached an "equilibrium state", where the
availability of empty niches is not saturated. We speculate that this result emerge
becausethe only extant clades that are nocturnal flying animals and could potentially
compete with bats for available niches are owls and nightjars (Simmons 2005). However,
these birds areonly carnivorous or insectivorous and, consequently, do not present the
huge trophic diversity of bats (Simmons 2005).
We here showed that the availability of ecological niches is the most important
mechanism to explain bats diversity dynamics over deep time. A very interesting step
forward is to understand how this mechanism drives diversity dynamics over time as well
as over geography (see Wiens 2011). For this, it will be necessary to develop a more
complex framework that simultaneously evaluates how lineage competition for niche
space varies through time as well as across geographic space. Even so, a simple and quick
solution would be to reconstruct ancestral states and fit models for subclades that are
consistently structured in geographic space. For example, fitting models for
Phylostomidae, which are a fully Neotropical clade, may change the best-fit model ifthe
Andes uplift had an important effect in diversification rates of this bat family, as
demonstrated for other groups of Neotropical clades (Fjeldså et al. 2012, Maestri and
Patterson 2016).
In conclusion, we highlight the greater importance of niche availability compared to
purely environmental changes in determining the diversity dynamics of bats. Accordingly,
competition among bat lineages for available niches along the Cenozoic era was more
crucial for bats diversification than the direct effect of major environmental events, such
as climate changes or mountain uplifts. Moreover, we also showed that bat's clade its still
increasing and has not yet reached their potential equilibrium diversity, suggesting more
niches may be available for occupation in the future, at least under current ecological and
biogeographical conditions.
143
Acknowledgments
DMCCA and JNPL received a studentship from the Coordenação de Aperfeiçoamento
de Pessoal de Nível Superior (CAPES). JAFD-F has been continuously supported by CNPq
productivity grants. FV was supported by a BJT “Science without Borders” grant from
CNPq.
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lineages. Journal of Evolutionary Biology, 27(10), 2204-2218.
Yule, G. U. (1925). A mathematical theory of evolution, based on the conclusions of Dr. JC
Willis, FRS. Philosophical transactions of the Royal Society of London. Series B,
containing papers of a biological character, 213, 21-87.
Zachos, J. C., Dickens, G. R., &Zeebe, R. E. (2008). An early Cenozoic perspective on
greenhouse warming and carbon-cycle dynamics. Nature, 451(7176), 279-283.
148
Conclusão Geral
Quais são os fatoresmais importantes que determinam a riqueza global de espécies de
morcegos entre regiões e diferentes intervalos de tempo? Nós concluímos que processos
ambientais atuando em grandes escalas geográficas - i.e. Energia, Heterogeneidade
Ambiental e Sazonalidade - são extremamente importantespara explicar a riqueza global
atual de espécies de morcegos na Terra. Além disso, a sinergia entre esses diferentes
processos ambientais são mais importantes para explicar a variação dessa riqueza de
espécies em diferentes regiões do que o efeito específico de cada um deles. Já para
explicar a variação na riqueza de espécies de morcegos ao longo do Cenozóico, nós
concluímos que o efeito indireto de processos ambientais, como o aumento na
temperatura global da Terra no início do Eoceno disponibilizando nichos vagos, foi mais
importante do que o efeito direto desses e outros processos ambientais. Pra finalizar, nós
também concluímos que incertezas associadas aos dados, erros estatísticos associados aos
modelos matemáticos, assim como a falta de conhecimento dos mecanismos ecológico-
evoutivos subjacentes aos modelos, podem afetar ou simplificar as nossas conclusões a
respeito dos padrões globais de riqueza de espécies.
149
Apêndice 1 (referente ao capítulo 1)
Table 1.Mean correlations between the variables within each hypothesis and their mean.
Ener represents the variables from the Energy hypothesis. Heter represents the variables
from the Heterogeneity hypothesis. And Seas represents the variables from the
Seasonality hypothesis.
Ener Heter Seas Mean
r 0.44 0.39 0.17 0.33
Table 2. Correlations between variables of the Energy and Heterogeneity hypotheses. The
variables from the Energy hypothesis were: mean temperature (M_temp), mean
precipitation (M_prec) and mean net primary productivity (M_npp). The variables from
the Heterogeneity hypothesis were: standard deviation of elevation (Sd_elev), standard
deviation of net primary productivity (Sd_npp), standard deviation of the mean
temperature (Sd_m_temp) and standard deviation of the mean precipitation
(Sd_m_prec).
Sd_elev Sd_npp Sd_m_temp Sd_m_prec
M_temp -0.06 0.35 0.08 0.26
M_prec 0.03 0.62 -0.01 0.65
M_npp -0.03 0.55 -0.04 0.41
150
Table 3. Correlations between variables of the Energy and Seasonality hypotheses. The
variables from the Energy hypothesis were: mean temperature (M_temp), mean
precipitation (M_prec) and mean net primary productivity (M_npp). The variables from
the Seasonality hypothesis were: standard deviation of temperature (Sd_temp) and
coefficient of variation of precipitation (Cv_prec).
Sd_temp Cv_prec
M_temp -0.86 0.35
M_prec -0.54 -0.21
M_npp -0.61 -0.14
Table 4. Correlations between variables of the Heterogeneity and Seasonality hypotheses.
The variables from the Heterogeneity hypothesis were: standard deviation of elevation
(Sd_elev), standard deviation of net primary productivity (Sd_npp), standard deviation of
the mean temperature (Sd_m_temp) and standard deviation of the mean precipitation
(Sd_m_prec). The variables from the Seasonality hypothesis were: standard deviation of
temperature (Sd_temp) and coefficient of variation of precipitation (Cv_prec).
Sd_temp Cv_prec
Sd_elev -0.08 0.1
Sd_npp -0.53 -0.08
Sd_m_temp -0.05 0.09
Sd_m_prec -0.44 -0.014
Table 5. Mean correlations between the Energy, Heterogeneity and Seasonality
hypotheses and their mean.
151
Ener_Heter Ener_Seas Heter_Seas Mean
r 0.26 0.46 0.18 0.29
Apêndice 2.1 (referente ao capítulo 2.1)
Evolutionary hypotheses for the latitudinal diversity gradient
Several hypotheses have beenproposed to understand why species richness is higher in
tropical regions (hereafter, TR) than in extratropical regions (hereafter ER; Mittelbach et
al., 2007; Roy & Goldberg, 2007). We presented nine such hypotheses on Table 1 of the
main text and here we provide a brief explanation of each of these hypotheses. Note that
the last three hypotheses in Table 1 (main text) were proposed and named based on
results from other studies that have used GeoSSE to understand geographical gradients of
species richness.
Pure Dispersal hypothesis
The Pure Dispersal hypothesis explains the LDG by the simple dispersal of species between
ER to TR due to resource availability and/or favorable abiotic conditions, without invoking
differences in speciation or extinction rates. This is a very used explanation for the
gradient and is based solely on contemporary processes, such as climate (see Hawkins et
al., 2003).
Source-Sink hypothesis
This hypothesis postulates that both regions, TR and ER, have the same rate of extinction
but different speciation and dispersal rates. Under this hypothesis, TR is the “center of
origin” of the majority of the lineages and supply ER with species, thus speciation and
dispersal rates are higher in TR than in ER (Goldberg et al., 2005).
Evolutionary Speed hypothesis
152
Similar to the Source-Sink hypothesis, the Evolutionary Speed hypothesis postulates that
both regions, TR and ER, have the same extinction rate and that TR is the species' “center
of origin” (i.e. higher speciation rate) caused by higher solar radiation accelerating
biological rates (Allen et al., 2007). However, under this hypothesis, species could
emigrate from TR equally as they emigrate from ER (same dispersal rate between regions;
Rohde, 1992).
Environmental Stability hypothesis
This hypothesis is based on the premise that TR has been more stable than ER
during the Cenozoic era (i.e. 65 million years before present; Mannion et al., 2014).
Consequently, TR and ER may have had similar speciation but differential extinction rates,
with TR having lower extinction rates due to a higher stability. In addition, TR could supply
ER with species (higher TR dispersal) or dispersal could be equal between both regions
(also known as Wallace hypothesis; Roy & Goldberg, 2007).
Out-of-the-Tropics hypothesis
The out of the tropics hypothesis posits that most lineages originated in TR and have
expanded into ER without leaving the TR. Therefore, TR has higher speciation and
dispersal rates and lower extinction rate than ER, leading to a higheraccumulation of
species in TR (Jablonski et al., 2006).
Tropical Niche-Conservatism hypothesis
The tropical niche conservatism is based on three premises: i) most lineages have
originated in the TR; ii) TR are older than ER (at least in the Cenozoic, since they were
more stable) and this has permitted more time for speciation events (“time-for-
speciation” effect; Pianka, 1966; Stephens & Wiens, 2003) and iii) species tend to conserve
their ancestral niche preferences for tropical conditions (i.e. tropical niche conservatism).
Although the original formulation of this hypothesis (Wiens & Donoghue, 2004) did not
make specific predictions on macroevolutionary rates, it implicitly assumed equal
speciation and extinction rates between TR and ER with elapsed time (i.e. period of
153
lineage occupation) being the main difference and either low or equal dispersal rates
between these regions (Rolland et al. 2014).
Into-the-Tropics 1
With the availability of GeoSSE, the LDG has been revisited for several taxonomic
groups (see Pyron & Wiens [2013] for amphibians; Pyron [2014] for squamates, Rolland et
al. [2014] for mammals). Some of the results from these studies were incongruent with
the traditional explanations and new evolutionary hypotheses were suggested. For
example, Pyron & Wiens (2013) found for amphibians a diversification pattern congruent
with the Out of the tropics’ explanation suggested by Jablonski et al. (2006), with TR
presenting higher speciation and lower extinction than ER. However, TR presented an
inverse dispersal pattern, with species historically moving from the extratropics into the
tropics. We called this hypothesis as Into-the-Tropics 1.
Into-the-Tropics 2
This unusual pattern of species biogeographically dispersing out of the extratropics
and into the tropics, as suggested by the Intro-the-Tropics 1 hypothesis, is also similar for
other taxa such as bats (Rolland et al. 2014) but with different speciation and extinction
rates. For bats, Rolland et al. (2014) suggested that the into-the-tropics dispersal pattern
could have been accompanied by similar speciation rates between TR and ER and lower
extinction rate in TR than ER. We called this hypothesis as Into-the-Tropics 2.
Into-the-Tropics 3
A third case of the Into-the-Tropics hypothesis was found for squamates (Pyron,
2014). For this group, GeoSSE analysis supported this Into-the-Tropics phenomenon
(higher dispersal from extratropics to the tropics) but with lower speciation and extinction
rates in TR than ER. We called this hypothesis as Into the tropics 3 (Pyron, 2014).
References
154
Allen AP, Gillooly JF, Savage VM, Brown JH. 2006. Kinetic effects of temperature on rates
of genetic divergence and speciation. Proceedings National Academy of Science of
the United States of America 103: 9130-9135.
Goldberg EE, Roy K, Lande R, Jablonski D. 2005. Diversity, endemism, and age distributions
in macroevolutionary sources and sinks. American Naturalist 165: 623-633.
Hawkins BA, Field R, Cornell HV, Currie DJ, Guégan JF, Kaufman DM, Kerr J, Mittelbach G,
Oberdorff T, O’Brien E, Porter E, Turner JR. 2003. Energy, water, and broad-scale
geographic patterns of species richness. Ecology 84: 3105-3117.
Jablonski D, Roy K, Valentine JW. 2006. Out of the tropics: evolutionary dynamics of the
latitudinal diversity gradient. Science 314: 102-106.
Mannion PD, Upchurch P, Benson RB, Goswami A. 2014. The latitudinal biodiversity
gradient through deep time. Trends Ecology and Evolution 29: 42-50.
Mittelbach GG, Schemske DW, Cornell HV, Allen AP, Brown JM, Bush MB, Harrison S,
Hurlbert A, Knowlton N, Lessios H, McCain C, McCune A, McDade L, McPeek M, Near
T, Price T, Ricklefs R, Roy K, Sax D, Schluter D, Sobel J, Turelli, M. 2007. Evolution and
the latitudinal diversity gradient: speciation, extinction and biogeography. Ecology
Letters 10: 315-331.
Pianka ER. 1966. Latitudinal gradients in species diversity: a review of concepts. American
Naturalist 100: 33-46.
Rohde K. 1992. Latitudinal gradients in species diversity: the search for the primary
cause. Oikos 65: 514-527.
Roy K, Goldberg EE. 2007. Origination, extinction, and dispersal: integrative models for
understanding present‐day diversity gradients. American Naturalist 170: S71-S85.
Stephens PR, Wiens JJ. 2003. Explaining species richness from continents to communities:
the time‐for‐speciation effect in emydid turtles. American Naturalist 161: 112-128.
155
Other simulation analyses to test GeoSSE for model inadequacy
Our main model inadequacy analysis consisted in a "null hypothesis" scenario based on a
simulated trait-independent phylogeny and random traits. However, to test GeoSSE for
model inadequacy based on others "null hypothesis" scenarios (according to Rabosky&
Goldberg, 2015), we created two alternative datasets: one using empirical phylogenies
and simulating neutral traits (EN dataset), and, another, using empirical phylogenies and
simulating random traits (ER dataset). For both datasets, we used 100 bat's
pseudoposterior phylogenies from Kuhn et al. (2011), which allowed us to analyze how
phylogenetic uncertainty - caused by the birth-death model to "break" polytomies -
affected GeoSSE Type 1 Error rates. In the EN and ER datasets, we simulated 100 neutral
three-states traits under a continuous-time discrete state Markov process for each
phylogeny under four transition rates: 0.05, 0.1, 1 and 10. But, for the ER dataset, we
reshuffled the tips across the states for each phylogeny to generate random traits. We
only used neutral and random traits that had more than 10% of species on each state.
Thus, at the end, we generated 10000 simulations (100 traits x 100 phylogenies) for each
"null hypothesis" scenario.
After the creation of both datasets to built alternative "null hypothesis" scenarios, we
fitted two GeoSSE models to each simulation: i) a null model where speciation and
extinction were constrained to be equal across character states (St = Se; Xt = Xe) while
dispersal was potentially asymetric (Dt De), and ii) an alternative model where
extinction rates were constrained to be equal across states (Xt = Xe) but speciation and
dispersal rates were potentially asymmetric (St Se; Dt De). We used the "Likelihood
Ratio Test" with a significance level of 0.05 to test GeoSSE for inflated Type 1 Error rates. If
GeoSSE incorrectly rejected the null hypothesis, the model was considered inadequate to
test macroevolutionary hypothesis. We used the R packages diversitree (FitzJohn, 2012)
and phytools (Revell, 2012) to create the functions to evaluate GeoSSE for Type 1 Error
rates.
156
In accordance with the dataset presented in the main text based on a trait-independent
phylogeny and random trait, both EN and ER datasets also showed that GeoSSE suffers
from model inadequacy. Our results showed that GeoSSE presented inflated Type 1 Error
rates for almost 100% of the simulations for all trait's transition rates (first row in Figures 1
and 2). Moreover, when including phylogenetic uncertainty on the analyses, ours results
showed that almost all bat phylogenies presented almost 100% of simulations with Type 1
Error (second row in Figures 1 and 2). The exceptions were for trait's transition rate of
0.05, where all phylogenies of the EN dataset presented 85% or more of simulations with
Type 1 Errors, and all phylogenies of the ER dataset presented 90% or more of simulations
with Type 1 Errors.
Figure 1. Type 1 Error rates for GeoSSE with a "null hypothesis" scenario based on bat's empirical
phylogenies and neutral traits. Neutral traits were simulated under four transition rates: 0.05, 0.1,
1 and 10. First row represents the distribution of the proportion of all simulations by p-values (red
157
dotted lines represent significance level of 0.05). Second row represents the distribution of the
proportion of phylogenies by the proportion of simulations with p-values lesser than 0.05.
Figure 2. Type 1 Error rates for GeoSSE with a "null hypothesis" scenario based on bat's empirical
phylogenies and random traits. To generate each random trait, we first generated neutral traits
and then reshuffled, for each phylogeny, the tips across the states. Neutral traits were simulated
under four transition rates: 0.05, 0.1, 1 and 10. First row represents the distribution of the
proportion of all simulations by p-values (red dotted lines represent significance level of 0.05)..
Second row represents the distribution of the proportion of phylogenies by the proportion of
simulations with p-values lesser than 0.05.
References
FitzJohn, RG. 2012. Diversitree: Comparative phylogenetic analyses of diversification in R.
Methods in Ecology and Evolution 3: 1084-1092.
Kuhn TS, Mooers AØ, Thomas GH. 2011. A simple polytomy resolver for dated
phylogenies. Methods in Ecology and Evolution 2: 427-436.
158
Rabosky DL, Goldberg EE. 2015. Model inadequacy and mistaken inferences of trait-
dependent speciation. Systematic Biology 64: 127-136.
Revell LJ. 2012. phytools: an R package for phylogenetic comparative biology (and other
things). Methods in Ecology and Evolution 3: 217-223.
Model inadequacy functions (R scripts)
#Script:
#1- geoTOE: function to test GeoSSE for inflated Type I Error using random traits
#2- geoTOE_neutral: function to test GeoSSE for inflated Type I Error using neutral traits
#3- Analyses of model inadequacy made on Alves et al. (2016)
#===================================================================#
#1- geoTOE:
#Type I error rates for "Geographic State, Speciation and Extinction" model
#(GeoSSE) using random traits
library("phytools")
library("diversitree")
library("geiger")
library("parallel")
##Description:
#Test type I error rates for GeoSSE by using random traits simulated on empirical and/or #simulated phylogenies and computing the probabilities (p-values) of Likelihood Ratio Tests #(LRT) under a chi-square distribution.
##Usage:
159
#geoTOE<- function(PHYLO, n.sim, trans.rates, dir)
geoTOE<- function(PHYLO, n.sim=10, trans.rates = tr, dir='results'){
require("diversitree")
require("phytools")
require("parallel")
if(!file.exists(dir))dir.create(dir)
setwd(dir)
n.cores<-detectCores()-2
cl <- makeCluster(getOption("cl.cores",n.cores))
n<-length(PHYLO)
time<-numeric(n)
for (i in 1:n){
time[i]<-system.time({
phy<- PHYLO[[i]]
start.point<- starting.point.geosse(phy)
sim.traits<-parallel::parSapply(cl=cl, X=1:n.sim,FUN=function(x,phy,Q1){#trait evolution
nostop<-FALSE
while(!nostop) {#while: repeat the code until the condition(!while) is not met
sim<- phytools::sim.history(tree=phy, Q=Q1, anc=NULL, nsim=1)$states#trait simulation
t.sim<- table(sim)
nostop<- all((t.sim/length(sim))>0.1)&length(t.sim)==3 #conditon: all states with more than 10% and the presence of three states
}
z<-sample(as.numeric(sim))
names(z)<-phy$tip.label
z
160
},
phy,Q1=trans.rates)
fit <- parApply(cl=cl,X=sim.traits,MARGIN=2,
FUN=function(x,tree,sp){#model's fit
y <- diversitree::make.geosse(tree=tree,states=x,sampling.f=NULL)
z1 <- diversitree::constrain(y, sAB ~ 0, xA ~ xB)#alternative model (1)
m1 <- stats::logLik(diversitree::find.mle(z1, sp[c(-3,-5)]))
w1 <- diversitree::constrain(y, sA ~ sB, sAB ~ 0, xA ~ xB)#null model #(2)
m2 <- stats::logLik(diversitree::find.mle(w1, sp[c(-2,-3,-5)]))
z <- c(m2,m1)},
tree=phy,sp=start.point)
p.values<- apply(fit,2,function(x)stats::pchisq (q=-2*x[1]+2*x[2],df=1,lower.tail=FALSE))#p-value
ft<-t(fit)
colnames(ft)<-c('null','alt')
fim<- cbind(ft,p.values)
write.table(fim,paste('simu_',i,'.txt',sep=''))
})[3]
}
stopCluster(cl)
setwd('..')
}
##Arguments:
#PHYLO: Ultrametric bifurcating phylogenetic trees, in ape "multiPhylo" format.
161
#n.sim: Number of simulations of a stochastic trait.
#trans.rates: Transition rates of a discrete trait with three states: 0, 1, 2. The object is a Q #matrix where rows or columns sum to 0 (see function "sim.history" in package "phytools";" #<https://cran.r-#project.org/web/packages/phytools/phytools.pdf>).
#dir: Name of the directory where the results should be stored.
##Details:
#This function have three steps: i) simulation of stochastic traits evolving under a continuous-#time discrete-state Markov process (with a reshuffled of the tips across the states); ii) #calibration of two GeoSSE models: "null" (s1 = s2; s12 = 0; x1 = x2; d12 x d21) and #"alternative" (s1 x s2; s21 = 0; x1 = x2; d12 x d21); and iii) computation of the probability of #LRT under a chi-square distribution for each simulation (trait and phylogeny).
##Values:
#geoTOE returns a matrix for each phylogeny (rows = simulated traits):
#Column 1: Loglikelihood of the "null" model.
#Column 2: Loglikelihood of the "alternative"" model.
#Column 3: Probability of the LRT for a given simulated trait of a given phylogeny.
##Authors:
#Davi M. C. C. Alves & Luciano F. Sgarbi
##References:
#Davis M.P., Midford P.E., Maddison W. 2013. Exploring power and parameter estimation of the BiSSE method for analyzing species diversification. BMC Evol. Biol. 13:38.
#FitzJohn R.G., Maddison W.P., and Otto S.P. 2009. Estimating trait-dependent speciation and extinction rates from incompletely resolved phylogenies. Syst. Biol. 58:595-611.
162
#Goldberg E.E., Lancaster L.T., and Ree R.H. 2011. Phylogenetic inference of reciprocal effects between geographic range evolution and diversification. Syst. Biol. 60:451-465.
#Maddison W.P., Midford P.E., and Otto S.P. 2007. Estimating a binary character's effect on speciation and extinction. Syst. Biol. 56:701-710.
#Rabosky D. L., Goldberg, E. E. 2015. Model Inadequacy and Mistaken Inferences of Trait-Dependent Speciation. Syst. Biol.64:127-136.
#=========================================================================#
#2- geoTOE_neutral:
#Type I error rates for "Geographic State, Speciation and Extinction" #model (GeoSSE) using neutral traits
library("phytools")
library("diversitree")
library("geiger")
library("parallel")
##Description:
#Test type I error rates for GeoSSE by using neutral traits simulated on empirical and/or #simulated phylogenies and computing the probabilities (p-values) of Likelihood Ratio Tests #(LRT) under a chi-square distribution.
##Usage:
#geoTOE_neutral<- function(PHYLO, n.sim, trans.rates, dir)
geoTOE_neutral<- function(PHYLO, n.sim=10, trans.rates = tr, dir='results'){
require("diversitree")
require("phytools")
163
require("parallel")
if(!file.exists(dir))dir.create(dir)
setwd(dir)
n.cores<-detectCores()-2
cl <- makeCluster(getOption("cl.cores",n.cores))
n<-length(PHYLO)
time<-numeric(n)
for (i in 87:n){
time[i]<-system.time({
phy<- PHYLO[[i]]
start.point<- starting.point.geosse(phy)
sim.traits<-parallel::parSapply(cl=cl, X=1:n.sim,FUN=function(x,phy,Q1){#trait evolution
nostop<-FALSE
while(!nostop) {#while: repeat the code until the condition(!while) is not met
sim<- phytools::sim.history(tree=phy, Q=Q1, anc=NULL, nsim=1)$states#trait simulation
t.sim<- table(sim)
nostop<- all((t.sim/length(sim))>0.1)&length(t.sim)==3 #condition: all states with more #than 10% and the presence of three states
}
z<-as.numeric(sim)
names(z)<-phy$tip.label
z
},
phy,Q1=trans.rates)
fit <- parApply(cl=cl,X=sim.traits,MARGIN=2,
FUN=function(x,tree,sp){#model's fit
164
y <- diversitree::make.geosse(tree=tree,states=x,sampling.f=NULL)
z1 <- diversitree::constrain(y, sAB ~ 0, xA ~ xB)#alternative model (1)
m1 <- stats::logLik(diversitree::find.mle(z1, sp[c(-3,-5)]))
w1 <- diversitree::constrain(y, sA ~ sB, sAB ~ 0, xA ~ xB)#null model #(2)
m2 <- stats::logLik(diversitree::find.mle(w1, sp[c(-2,-3,-5)]))
z <- c(m2,m1)},
tree=phy,sp=start.point)
p.values<- apply(fit,2,function(x)stats::pchisq (q=-2*x[1]+2*x[2],df=1,lower.tail=FALSE))
#p-value
ft<-t(fit)
colnames(ft)<-c('null','alt')
fim<- cbind(ft,p.values)
write.table(fim,paste('simu_',i,'.txt',sep=''))
})[3]
}
stopCluster(cl)
setwd('..')
}
##Arguments:
#PHYLO: Ultrametric bifurcating phylogenetic trees, in ape "multiPhylo" format.
#n.sim: Number of simulations of a stochastic trait.
#trans.rates: Transition rates of a discrete trait with three states: 0, 1, 2. The object is a Q #matrix where rows or columns sum to 0 (see function "sim.history" in package "phytools";" #<https://cran.r-project.org/web/packages/phytools/phytools.pdf>).
165
#dir: Name of the directory where the results should be stored.
##Details:
#This function have three steps: i) simulation of stochastic traits evolving under a
#continuous-time discrete-state Markov process; ii) calibration of two GeoSSE models:
#"null" (s1 = s2; s12 = 0; x1 = x2; d12 x d21) and "alternative" (s1 x s2; s21 = 0;
#x1 = x2; d12 x d21); and iii) computation of the probability of LRT under a chi-square
#distribution for each simulation (trait and phylogeny).
##Values:
#geoTOE_neutral returns a matrix for each phylogeny (rows = simulated traits):
#Column 1: Loglikelihood of the "null" model.
#Column 2: Loglikelihood of the "alternative"" model.
#Column 3: Probability of the LRT for a given simulated trait of a given phylogeny.
##Authors:
#Davi M. C. C. Alves & Luciano F. Sgarbi
##References:
#Davis M.P., Midford P.E., Maddison W. 2013. Exploring power and parameter estimation of the BiSSE method for analyzing species diversification. BMC Evol. Biol. 13:38.
#FitzJohn R.G., Maddison W.P., and Otto S.P. 2009. Estimating trait-dependent speciation and extinction rates from incompletely resolved phylogenies. Syst. Biol. 58:595-611.
#Goldberg E.E., Lancaster L.T., and Ree R.H. 2011. Phylogenetic inference of reciprocal effects between geographic range evolution and diversification. Syst. Biol. 60:451-465.
#Maddison W.P., Midford P.E., and Otto S.P. 2007. Estimating a binary character's effect on speciation and extinction. Syst. Biol. 56:701-710.
166
#Rabosky D. L., Goldberg, E. E. 2015. Model Inadequacy and Mistaken Inferences of Trait-Dependent Speciation. Syst. Biol.64:127-136.
#=========================================================================#
#3- Analyses of model inadequacy made on Alves et al. (2016)
library("phytools")
library("diversitree")
library("geiger")
library("parallel")
#traits (q = 0.05 -> 0.1 -> 1 -> 10)
(tr.05<-matrix(c(-0.05,0.025,0.025,0.025,-0.05,0.05,0.025,0.025,-0.05),3,3,dimnames=list(c(0,1,2),c(0,1,2))))
(tr.1<-matrix(c(-0.1,0.05,0.05,0.05,-0.1,0.05,0.05,0.05,-0.1),3,3,dimnames=list(c(0,1,2),c(0,1,2))))
(tr1<-matrix(c(-1,0.5,0.5,0.5,-1,0.5,0.5,0.5,-1),3,3,dimnames=list(c(0,1,2),c(0,1,2))))
(tr10<-matrix(c(-10,5,5,5,-10,5,5,5,-10),3,3,dimnames=list(c(0,1,2),c(0,1,2))))
#100 simulated phylogenies
sim.phy=list()
for(i in 1:100){
sim.phy[[i]]<- sim.bdtree(b=0.5,d=0,n=1054)
}
class(sim.phy)=c("multiPhylo")
#100 empirical phylogenies (Kuhn et al. 2011)
167
setwd("directory")
list.phy=list.files(path="directory")
emp.phy=lapply(list.phy,read.tree)
#Analyses
#Simulated phylogenies - random traits (geoTOE)
setwd("directory")
geoTOE(PHYLO=sim.phy,n.sim=1, trans.rates = tr.05, dir='t.05',sf=c(1,1,1))
geoTOE(PHYLO=sim.phy,n.sim=1, trans.rates = tr.1, dir='t.1',sf=c(1,1,1))
geoTOE(PHYLO=sim.phy,n.sim=1, trans.rates = tr1, dir='t1',sf=c(1,1,1))
geoTOE(PHYLO=sim.phy,n.sim=1, trans.rates = tr10, dir='t10',sf=c(1,1,1))
#Empirical phylogenies - random traits (geoTOE)
setwd("directory")
geoTOE(PHYLO=emp.phy,n.sim=100, trans.rates = tr.05, dir='t.05',sf=c(1,1,1))
geoTOE(PHYLO=emp.phy,n.sim=100, trans.rates = tr.1, dir='t.1',sf=c(1,1,1))
geoTOE(PHYLO=emp.phy,n.sim=100, trans.rates = tr1, dir='t1',sf=c(1,1,1))
geoTOE(PHYLO=emp.phy,n.sim=100, trans.rates = tr10, dir='t10',sf=c(1,1,1))
#Empirical phylogenies - neutral traits (geoTOE_neutral)
setwd("directory")
geoTOE_neutral(PHYLO=emp.phy,n.sim=100, trans.rates = tr.05, dir='t.05',sf=c(1,1,1))
geoTOE_neutral(PHYLO=emp.phy,n.sim=100, trans.rates = tr.1, dir='t.1',sf=c(1,1,1))
geoTOE_neutral2(PHYLO=emp.phy,n.sim=100, trans.rates = tr1, dir='t1',sf=c(1,1,1))
geoTOE_neutral(PHYLO=emp.phy,n.sim=100, trans.rates = tr10, dir='t10',sf=c(1,1,1))
168
Figure 3. Cumulative proportion of species on each trait (i.e. tropical, extratropical or
transtropical) according to 21 thresholds (i.e. percentage of 0-20%) of area of range overlap with
extratropical biome. First row corresponds to environmental trait and second row corresponds to
geographical trait.
169
Apêndice 2.2 (referente ao capítulo 2.2)
#---------------------------------------Introduction-------------------------------------------------#
#Explanation of the two functions used in the study to evaluate ClaSSE for inflated Type I Error rates, and, at the end, the analyses made in the study.
#-------------------------------------First function--------------------------------------------------#
#claTOE: Type I error rates for "Cladogenetic State change, Speciation and Extinction" model (ClaSSE) by simulating neutral traits
library("phytools")
library("diversitree")
library("geiger")
library("parallel")
##Description:
#Test type I error rates for ClaSSE by simulating neutral traits on a phylogeny, and computing, for
#each simulation, the probabilities (p-values) of Likelihood Ratio Test (LRT) of two models under a chi-square distribution.
claTOE<-function(phy, k, trans.rates, lAlt, lNull, ntraits=100){
n.cores<-detectCores()-2
cl <- makeCluster(getOption("cl.cores",n.cores))
start.point <- starting.point.classe(phy,k,eps=0.5)
170
sim.traits<-parallel::parSapply(cl=cl, X=1:ntraits,FUN=function(x,phy,Q1,k){#simulation of neutral traits
nostop<-FALSE
while(!nostop) {#while: repeat the code until the condition is met
sim <- phytools::sim.history(tree=phy, Q=Q1, anc=NULL, nsim=1)$states
t.sim <- table(sim)
nostop <- all((t.sim/length(sim))>0.08)&length(t.sim)==k #condition: only traits with states with more than 0.08% of spp. and the presence of seven states
}
z<-as.numeric(sim)
names(z)<-phy$tip.label
z
},
phy,Q1=trans.rates,k=k)
fit <- parApply(cl=cl,X=sim.traits,MARGIN=2,
FUN=function(trait,tree,sp,k,lAlt,lNull){#model's fit
y <- diversitree::make.classe(tree=tree,states=trait,k,sampling.f=NULL)
z1 <- diversitree::constrain(y, formulae=lAlt)#alternative model (1)
m1 <- stats::logLik(diversitree::find.mle(z1, sp[diversitree::argnames(z1)]))
w1 <- diversitree::constrain(y, formulae=lNull)#null model (2)
m2 <- stats::logLik(diversitree::find.mle(w1, sp[diversitree::argnames(w1)]))
z <- c(m2,m1)},
tree=phy,sp=start.point,k=k,lAlt=lAlt,lNull=lNull)
p.values <- apply(fit,2,function(x)stats::pchisq (q=-2*x[1]+2*x[2],df=1,lower.tail=FALSE))#p-values
ft<-t(fit)
171
colnames(ft)<-c('null','alt')
fim <- cbind(ft,p.values)
write.table(fim,'result.txt')
stopCluster(cl)
return(fim)
}
##Arguments:
#phy: Ultrametric bifurcating phylogenetic tree on ape "phylo" format.
#K: number of states.
#trans.rates: Transition rates of a discrete trait with k states. The object is a Q matrix where
#rows or columns sum to 0 (see function "sim.history" in package "phytools";" <https://cran.r-project.org/web/
#packages/phytools/phytools.pdf>).
#ntraits: Number of simulations of a stochastic trait.
#lAlt: a list of parameters constrains to build an alternative ClaSSE model.
#lNull: a list of parameters constrains to build a null ClaSSE model.
##Details:
#This function have three steps: i) simulation of stochastic traits evolving under a continuous-time discrete-state
#Markov process on a phylogenetic tree; ii) calibration of two ClaSSE models: "null" and "alternative";
172
#and iii) computation of the probability of LRT (for both models) under a chi-square distribution for each simulated trait.
##Values:
#geoTOE returns a matrix (rows = simulated traits):
#Column 1: Loglikelihood of the "null"" model.
#Column 2: Loglikelihood of the "alternative" model.
#Column 3: Probability of the LRT for a given simulated trait.
##Authors:
#Davi M. C. C. Alves & Luciano F. Sgarbi
##References:
#Davis M.P., Midford P.E., Maddison W. 2013. Exploring power and parameter estimation of the BiSSE method for analyzing species diversification. BMC Evol. Biol. 13:38.
#FitzJohn R.G., Maddison W.P., and Otto S.P. 2009. Estimating trait-dependent speciation and extinction rates from incompletely resolved phylogenies. Syst. Biol. 58:595-611.
#Goldberg E.E., Lancaster L.T., and Ree R.H. 2011. Phylogenetic inference of reciprocal effects between geographic range evolution and diversification. Syst. Biol. 60:451-465.
#Goldberg E.E., & Igić B. 2012. Tempo and mode in plant breeding system evolution. Evolution 66:3701-3709.
#Maddison W.P., Midford P.E., and Otto S.P. 2007. Estimating a binary character's effect on speciation and extinction. Syst. Biol. 56:701-710.
#Rabosky D. L., Goldberg, E. E. 2015. Model Inadequacy and Mistaken Inferences of Trait-Dependent Speciation. Syst. Biol.64:127-136.
#------------------------------------------Second function-----------------------------------------#
173
#claTOE2: Type I error rates for "Cladogenetic State change, Speciation and Extinction" model (ClaSSE) by simulating random traits
library("phytools")
library("diversitree")
library("geiger")
library("parallel")
##Description:
#Test type I error rates for ClaSSE by simulating random traits on a
#phylogeny, and computing, for each simulation, the probabilities (p-values) of Likelihood Ratio Test (LRT) of two models under a chi-square distribution.
claTOE2<-function(phy, k, trans.rates, lAlt, lNull, ntraits=100){
n.cores<-detectCores()-2
cl <- makeCluster(getOption("cl.cores",n.cores))
start.point <- starting.point.classe(phy,k,eps=0.5)
sim.traits<-parallel::parSapply(cl=cl, X=1:ntraits,FUN=function(x,phy,Q1,k){#simulation of neutral traits
nostop<-FALSE
while(!nostop) {#while: repeat the code until the condition is met
sim <- phytools::sim.history(tree=phy, Q=Q1, anc=NULL, nsim=1)$states
t.sim <- table(sim)
nostop <- all((t.sim/length(sim))>0.08)&length(t.sim)==k #condition: only traits with states with more than 0.08% of spp. and the presence of seven states
174
}
z<-sample(as.numeric(sim))#generating a trait with random values for the tips
names(z)<-phy$tip.label
z
},
phy,Q1=trans.rates,k=k)
fit <- parApply(cl=cl,X=sim.traits,MARGIN=2,
FUN=function(trait,tree,sp,k,lAlt,lNull){#model's fit
y <- diversitree::make.classe(tree=tree,states=trait,k,sampling.f=NULL)
z1 <- diversitree::constrain(y, formulae=lAlt)#alternative model (1)
m1 <- stats::logLik(diversitree::find.mle(z1, sp[diversitree::argnames(z1)]))
w1 <- diversitree::constrain(y, formulae=lNull)#null model (2)
m2 <- stats::logLik(diversitree::find.mle(w1, sp[diversitree::argnames(w1)]))
z <- c(m2,m1)},
tree=phy,sp=start.point,k=k,lAlt=lAlt,lNull=lNull)
p.values <- apply(fit,2,function(x)stats::pchisq (q=-2*x[1]+2*x[2],df=1,lower.tail=FALSE))#p-values
ft<-t(fit)
colnames(ft)<-c('null','alt')
fim <- cbind(ft,p.values)
write.table(fim,'result.txt')
stopCluster(cl)
return(fim)
}
175
##Arguments:
#phy: Ultrametric bifurcating phylogenetic tree on ape "phylo" format.
#K: number of states.
#trans.rates: Transition rates of a discrete trait with k states. The object is a Q matrix where
#rows or columns sum to 0 (see function "sim.history" in package "phytools";" <https://cran.r-project.org/web/
#packages/phytools/phytools.pdf>).
#ntraits: Number of simulations of a stochastic trait.
#lAlt: a list of parameters constrains to build an alternative ClaSSE model.
#lNull: a list of parameters constrains to build a null ClaSSE model.
##Details:
#This function have three steps: i) simulation of a trait with random values for the tips on a phylogenetic tree; ii) calibration of two ClaSSE models: "null" and "alternative";
#and iii) computation of the probability of LRT (for both models )under a chi-square distribution for each simulated trait.
##Values:
#geoTOE returns a matrix (rows = simulated traits):
#Column 1: Loglikelihood of the "null"" model.
#Column 2: Loglikelihood of the "alternative" model.
#Column 3: Probability of the LRT for a given simulated trait.
##Authors:
#Davi M. C. C. Alves & Luciano F. Sgarbi
176
##References:
#Davis M.P., Midford P.E., Maddison W. 2013. Exploring power and parameter estimation of the BiSSE method for analyzing species diversification. BMC Evol. Biol. 13:38.
#FitzJohn R.G., Maddison W.P., and Otto S.P. 2009. Estimating trait-dependent speciation and extinction rates from incompletely resolved phylogenies. Syst. Biol. 58:595-611.
#Goldberg E.E., Lancaster L.T., and Ree R.H. 2011. Phylogenetic inference of reciprocal effects between geographic range evolution and diversification. Syst. Biol. 60:451-465.
#Goldberg E.E., & Igić B. 2012. Tempo and mode in plant breeding system evolution. Evolution 66:3701-3709.
#Maddison W.P., Midford P.E., and Otto S.P. 2007. Estimating a binary character's effect on speciation and extinction. Syst. Biol. 56:701-710.
#Rabosky D. L., Goldberg, E. E. 2015. Model Inadequacy and Mistaken Inferences of Trait-Dependent Speciation. Syst. Biol.64:127-136.
#-----------------------------------Performance analyses-----------------------------------------#
#trait's transition rate (Q matrix)
(tr<-matrix(c(-1,0.5,0.1,0.1,0.1,0.1,0.1,0.5,-1,0.1,0.1,0.1,0.1,0.1,0.5,0.1,-1,0.1,0.1,0.1,0.1,0.5,0.1,0.1,-1,0.1,0.1,0.1,0.5,0.1,0.1,0.1,-1,0.1,0.1,0.5,0.1,0.1,0.1,0.1,-1,0.1,0.5,0.1,0.1,0.1,0.1,0.1,-1),7,7,dimnames=list(c(1,2,3,4,5,6,7),c(1,2,3,4,5,6,7))))
#phylogenies
(emp.phy<-read.tree("empirical bird phylogeny only with spp. with genetic data"))#empirical phylogeny with 6670 bird spp.
(sim.phy<-sim.bdtree(b=0.5,d=0,n=6670))#simulated phylogeny under a Yule diversification model
#analyses
177
(result1 = claTOE(phy=emp.phy, k=7, trans.rates=tr, lAlt=par.alt, lNull=par.null, ntraits=100))#for the EN dataset (see manuscript)
(result2 = claTOE2(phy=emp.phy, k=7, trans.rates=tr, lAlt=par.alt, lNull=par.null, ntraits=100))#for the ER dataset (see manuscript)
(result3 = claTOE2(phy=sim.phy, k=7, trans.rates=tr, lAlt=par.alt, lNull=par.null, ntraits=100))# for the SR dataset (see manuscript)
# It takes about 55 hours to run each analysis for Birds (6670 spp.)
178
Apêndice 3 (referente ao capítulo 4)
Table 1. Selecting the best diversification model across all the models representing the
macroevolutionary hypotheses for bats diversity dynamics through deep time based on
"Jone's phylogeny". The models were: "con-Spe" = constant speciation, "con-Spe; con-Ext"
= constant speciation and extinction, "exp-Spe" = exponential relationship between
speciation with its causal factor, " exp-Spe; con-Ext" =exponential relationship between
speciation with its causal factor and constant extinction, "con-Spe; exp-Ext" = exponential
relationship between extinction with its causal factor and constant speciation, "exp-Spe;
exp-Ext" = exponential relationship between speciation and extinction with its causal
factor, "lin-Spe" = linear relationship between speciation with its causal factor, "lin-Spe;
con-Ext" = linear relationship between speciation with its causal factor and constant
extinction, "con-Spe; lin-Ext" = linear relationship between extinction with its causal factor
and constant speciation, "lin-Spe; lin-Ext" = linear relationship between speciation and
extinction with its causal factor. AICc = sample-size corrected Akaike Information
Criterion, ΔAIC = delta Akaike Information Criterion and AICw = weight Akaike Information
Criterion.
Hypotheses Models AICc ΔAIC AICw
Null 1 con-Spe 6746.92 2571.34 0
Null 2 con-Spe; con-Ext 6744.53 2568.95 0
Time exp-Spe 6726.95 2551.37 0
exp-Spe; con-Ext 6728.96 2553.38 0
con-Spe; exp-Ext 6734.29 2558.71 0
exp-Spe; exp-Ext 6730.97 2555.35 0
lin-Spe 6727.06 2551.48 0
lin-Spe; con-Ext 6729.07 2553.43 0
con-Spe; lin-Ext 6725.28 2549.7 0
179
lin-Spe; lin-Ext 6703.06 2527.48 0
Environmental Climate
change
(temperature)
exp-Spe 6741.19 2565.61 0
exp-Spe; con-Ext 6743.20 2567.62 0
con-Spe; exp-Ext 6735.63 2560.05 0
exp-Spe; exp-Ext 6732.74 2557.16 0
lin-Spe 6739.28 2563.7 0
lin-Spe; con-Ext 6741.29 2565.71 0
con-Spe; lin-Ext 6728.69 2553.10 0
lin-Spe; lin-Ext 6712.25 2536.66 0
Environmental Sea-level exp-Spe 6746.07 2570.49 0
exp-Spe; con-Ext 6746.59 2571 0
con-Spe; exp-Ext 6737.41 2561.83 0
exp-Spe; exp-Ext 6733.47 2557.89 0
lin-Spe 6744.93 2569.35 0
lin-Spe; con-Ext 6746.37 2570.79 0
con-Spe; lin-Ext 6731.91 2556.32 0
lin-Spe; lin-Ext 6720.4 2544.82 0
Environmental Andean Uplift exp-Spe 6726.77 2551.19 0
exp-Spe; con-Ext 6728.79 2553.21 0
con-Spe; exp-Ext 6724.99 2549.41 0
exp-Spe; exp-Ext 6728.74 2553.16 0
lin-Spe 6724.35 2548.77 0
lin-Spe; con-Ext 6726.36 2550.78 0
con-Spe; lin-Ext 6720.38 2544.8 0
lin-Spe; lin-Ext 6727.09 2551.51 0
Niche
Availability
lin-Spe 6213.54 2037.96 0
lin-Spe; con-Ext 6791.08 2615.5 0
exp-Spe; con-Ext 8229.21 4053.63 0
lin-Spe; lin-Ext 4175.58 0 1
180
Table 2. Selecting the best diversification model across all the models representing the
macroevolutionary hypotheses for bats diversity dynamics through deep time based on
"Shi's phylogeny". The models were: "con-Spe" = constant speciation, "con-Spe; con-Ext" =
constant speciation and extinction, "exp-Spe" = exponential relationship between
speciation with its causal factor, " exp-Spe; con-Ext" =exponential relationship between
speciation with its causal factor and constant extinction, "con-Spe; exp-Ext" = exponential
relationship between extinction with its causal factor and constant speciation, "exp-Spe;
exp-Ext" = exponential relationship between speciation and extinction with its causal
factor, "lin-Spe" = linear relationship between speciation with its causal factor, "lin-Spe;
con-Ext" = linear relationship between speciation with its causal factor and constant
extinction, "con-Spe; lin-Ext" = linear relationship between extinction with its causal factor
and constant speciation, "lin-Spe; lin-Ext" = linear relationship between speciation and
extinction with its causal factor. AICc = sample-size corrected Akaike Information
Criterion, ΔAIC = delta Akaike Information Criterion and AICw = weight Akaike Information
Criterion.
Hypotheses Models AICc ΔAIC AIC
w
Null 1 con-Spe 6122.71 1361.13 0
Null 2 con-Spe; con-Ext 6124.71 1363.13 0
Time exp-Spe 6080.09 1318.51 0
exp-Spe; con-Ext 6082.1 1320.52 0
con-Spe; exp-Ext 6126.73 1365.15 0
exp-Spe; exp-Ext 6083.81 1322.23 0
lin-Spe 6078.08 1316.5 0
lin-Spe; con-Ext 6080.1 1318.52 0
con-Spe; lin-Ext 6126.93 1365.35 0
lin-Spe; lin-Ext 6078.82 1317.24 0
181
Environmenta
l
Climate
change
(temperature
)
exp-Spe 6077.79 1316.21 0
exp-Spe; con-Ext 6079.81 1318.23 0
con-Spe; exp-Ext 6126.93 1365.35 0
exp-Spe; exp-Ext 6081.83 1320.25 0
lin-Spe 6076.2 1314.62 0
lin-Spe; con-Ext 6078.22 1316.64 0
con-Spe; lin-Ext 6126.93 1365.35 0
lin-Spe; lin-Ext 6078.65 1317.07 0
Environmenta
l
Sea-level exp-Spe 6092.13 1330.55 0
exp-Spe; con-Ext 6094.12 1332.54 0
con-Spe; exp-Ext 6126.93 1365.35 0
exp-Spe; exp-Ext 6096.17 1334.59 0
lin-Spe 6090.12 1328.54 0
lin-Spe; con-Ext 6092.13 1330.55 0
con-Spe; lin-Ext 6126.93 1365.35 0
lin-Spe; lin-Ext 6094.15 1332.57 0
Environmenta
l
Andean
Uplift
exp-Spe 6081.22 1319.64 0
exp-Spe; con-Ext 6083.23 1321.65 0
con-Spe; exp-Ext 6126.93 1365.35 0
exp-Spe; exp-Ext 6085.18 1323.6 0
lin-Spe 6079.75 1318.17 0
lin-Spe; con-Ext 6081.76 1320.18 0
con-Spe; lin-Ext 6126.93 1365.35 0
lin-Spe; lin-Ext 6083.25 1321.67 0
Niche
Availability
lin-Spe 6469.57 1707.99 0
lin-Spe; con-Ext 6137.56 1375.98 0
exp-Spe; con-Ext 4761.58 0 1
lin-Spe; lin-Ext 6106.73 1345.15 0
182
Table 3. Ten diversification models representing the Null 1, Null2 and Time hypotheses
based on "Jones' phylogeny". The models were: "con-Spe" = constant speciation, "con-
Spe; con-Ext" = constant speciation and extinction, "exp-Spe" = exponential relationship
between speciation with its causal factor, " exp-Spe; con-Ext" =exponential relationship
between speciation with its causal factor and constant extinction, "con-Spe; exp-Ext" =
exponential relationship between extinction with its causal factor and constant speciation,
"exp-Spe; exp-Ext" = exponential relationship between speciation and extinction with its
causal factor, "lin-Spe" = linear relationship between speciation with its causal factor, "lin-
Spe; con-Ext" = linear relationship between speciation with its causal factor and constant
extinction, "con-Spe; lin-Ext" = linear relationship between extinction with its causal factor
and constant speciation, "lin-Spe; lin-Ext" = linear relationship between speciation and
extinction with its causal factor. NP = number of parameters; logL = loglikelihood; AICc =
sample-size corrected Akaike Information Criterion; Lambda = speciation rate; Alpha = the
regression coefficient between speciation and time; Mu = extinction rate; Beta = the
regression coefficient between extinction and time. The best model is in bold.
Models NP logL AICc Lambda Alpha Mu Beta
con-Spe 1 -3372.46 6746.92 0.123 - - -
con-Spe; con-Ext 2 - 3370.26 6744.53 0.137 - 0.027 -
exp-Spe 2 -3361.47 6726.95 0.139 -0.014 - -
exp-Spe; con-Ext 3 -3361.47 6728.96 0.139 -0.014 0 -
con-Spe; exp-Ext 3 -3364.13 6734.29 0.137 - 0.017 0.032
exp-Spe; exp-Ext 4 -3361.47 6730.97 0.139 -0.014 0 0.039
lin-Spe 2 -3361.52 6727.06 0.136 -0.001 - -
lin-Spe; con-Ext 3 -3361.52 6729.07 0.137 -0.001 0 -
con-Spe; lin-Ext 3 -3359.63 6725.28 0.131 - 0.005 -0.002
lin-Spe; lin-Ext 4 -3347.51 6703.06 0.079 0.037 0.066 -0.036
183
Table 4. Eight environmental-dependent diversification models representing the Climate
change hypothesis based on "Jones' phylogeny". The models were: "exp-Spe" =
exponential relationship between speciation with its causal factor, " exp-Spe; con-Ext"
=exponential relationship between speciation with its causal factor and constant
extinction, "con-Spe; exp-Ext" = exponential relationship between extinction with its
causal factor and constant speciation, "exp-Spe; exp-Ext" = exponential relationship
between speciation and extinction with its causal factor, "lin-Spe" = linear relationship
between speciation with its causal factor, "lin-Spe; con-Ext" = linear relationship between
speciation with its causal factor and constant extinction, "con-Spe; lin-Ext" = linear
relationship between extinction with its causal factor and constant speciation, "lin-Spe;
lin-Ext" = linear relationship between speciation and extinction with its causal factor. NP =
number of parameters; logL = loglikelihood; AICc = sample-size corrected Akaike
Information Criterion; Lambda = speciation rate; Alpha = the regression coefficient
between speciation and temperature; Mu = extinction rate; Beta = the regression
coefficient between extinction and temperature. The best model is in bold.
Models NP logL AICc Lambda Alpha Mu Beta
exp-Spe 2 -3368.59 6741.19 0.14 -0.031 - -
exp-Spe; con-Ext 3 -3368.59 6743.20 0.14 -0.031 0 -
con-Spe; exp-Ext 3 -3364.80 6735.63 0.135 - 0.009 0.159
exp-Spe; exp-Ext 4 -3362.35 6732.74 0.108 0.102 0.047 0.155
lin-Spe 2 -3367.63 6739.28 0.146 -0.004 - -
lin-Spe; con-Ext 3 -3367.63 6741.29 0.146 -0.004 0 -
con-Spe; lin-Ext 3 -3361.33 6728.69 0.136 - 0.032 -0.009
lin-Spe; lin-Ext 4 -3352.10 6712.25 0.06 0.026 0.041 -0.03
Table 5. Eight environmental-dependent diversification models representing the Sea level
hypothesis based on "Jones' phylogeny". The models were: "exp-Spe" = exponential
relationship between speciation with its causal factor, " exp-Spe; con-Ext" =exponential
184
relationship between speciation with its causal factor and constant extinction, "con-Spe;
exp-Ext" = exponential relationship between extinction with its causal factor and constant
speciation, "exp-Spe; exp-Ext" = exponential relationship between speciation and
extinction with its causal factor, "lin-Spe" = linear relationship between speciation with its
causal factor, "lin-Spe; con-Ext" = linear relationship between speciation with its causal
factor and constant extinction, "con-Spe; lin-Ext" = linear relationship between extinction
with its causal factor and constant speciation, "lin-Spe; lin-Ext" = linear relationship
between speciation and extinction with its causal factor. NP = number of parameters; logL
= loglikelihood; AICc = sample-size corrected Akaike Information Criterion; Lambda =
speciation rate; Alpha = the regression coefficient between speciation and sea level; Mu =
extinction rate; Beta = the regression coefficient between extinction and sea level. The
best model is in bold.
Models NP logL AICc Lambda Alpha Mu Beta
exp-Spe 2 -3371.03 6746.07 0.119 -0.002 - -
exp-Spe; con-Ext 3 -3370.28 6746.59 0.132 0 0.021 -
con-Spe; exp-Ext 3 -3365.69 6737.41 0.135 - 0.025 0.015
exp-Spe; exp-Ext 4 -3362.72 6733.47 0.168 0.005 0.07 0.014
lin-Spe 2 -3370.46 6744.93 0.119 0 - -
lin-Spe; con-Ext 3 -3370.17 6746.370 0.129 0 0.016 -
con-Spe; lin-Ext 3 -3362.94 6731.91 0.136 - 0.028 0.001
lin-Spe; lin-Ext 4 -3356.18 6720.4 0.178 0.001 0.085 0.002
Table 6. Eight environmental-dependent diversification models representing the Andean
uplift hypothesis based on "Jones' phylogeny". The models were: "exp-Spe" = exponential
relationship between speciation with its causal factor, " exp-Spe; con-Ext" =exponential
relationship between speciation with its causal factor and constant extinction, "con-Spe;
exp-Ext" = exponential relationship between extinction with its causal factor and constant
speciation, "exp-Spe; exp-Ext" = exponential relationship between speciation and
185
extinction with its causal factor, "lin-Spe" = linear relationship between speciation with its
causal factor, "lin-Spe; con-Ext" = linear relationship between speciation with its causal
factor and constant extinction, "con-Spe; lin-Ext" = linear relationship between extinction
with its causal factor and constant speciation, "lin-Spe; lin-Ext" = linear relationship
between speciation and extinction with its causal factor. NP = number of parameters; logL
= loglikelihood; AICc = sample-size corrected Akaike Information Criterion; Lambda =
speciation rate; Alpha = the regression coefficient between speciation and andean uplift;
Mu = extinction rate; Beta = the regression coefficient between extinction and andean
uplift. The best model is in bold.
Models NP logL AICc Lambda Alpha Mu Beta
exp-Spe 2 -3361.38 6726.77 0.078 0 0 -
exp-Spe; con-Ext 3 -3361.38 6728.79 0.078 0 0 -
con-Spe; exp-Ext 3 -3359.48 6724.99 0.133 0 0.106 0
exp-Spe; exp-Ext 4 -3360.35 6728.74 0.08 0 0.022 -0.001
lin-Spe 2 -3360.17 6724.35 0.07 0 0 0
lin-Spe; con-Ext 3 -3360.17 6726.36 0.07 0 0 0
con-Spe; lin-Ext 3 -3357.18 6720.38 0.133 0 0.092 0
lin-Spe; lin-Ext 4 -3359.52 6727.09 0.077 0 0.02 0
Table 7. Four diversity-dependent diversification models representing the Niche
availability hypothesis based on "Jones' phylogeny". The models were: "exp-Spe; con-Ext"
= exponential relationship between speciation with its causal factor and constant
extinction, "lin-Spe" = linear relationship between speciation with its causal factor, "lin-
Spe; con-Ext" = linear relationship between speciation with its causal factor and constant
extinction, "lin-Spe; lin-Ext" = linear relationship between speciation and extinction with
its causal factor. NP = number of parameters; logL = loglikelihood; AICc = sample-size
corrected Akaike Information Criterion; Lambda = speciation rate; Mu = extinction rate; k
= carrying capacity. The best model is in bold.
186
Model NP logL AICc Lambda Mu K
exp-Spe; con-Ext 3 -4111.59 8229.21 3.855 0.026 1300
lin-Spe 2 -3104.77 6213.54 0.175 - 4773.76
lin-Spe; con-Ext 3 -3392.53 6791.08 0.271 0.137 1545.62
lin-Spe; lin-Ext 4 -2083.77 4175.58 0.5 0.499 20304.11
Table 8. Ten diversification models representing the Null 1, Null2 and Time hypotheses
based on "Shi's phylogeny". The models were: "con-Spe" = constant speciation, "con-Spe;
con-Ext" = constant speciation and extinction, "exp-Spe" = exponential relationship
between speciation with its causal factor, " exp-Spe; con-Ext" =exponential relationship
between speciation with its causal factor and constant extinction, "con-Spe; exp-Ext" =
exponential relationship between extinction with its causal factor and constant speciation,
"exp-Spe; exp-Ext" = exponential relationship between speciation and extinction with its
causal factor, "lin-Spe" = linear relationship between speciation with its causal factor, "lin-
Spe; con-Ext" = linear relationship between speciation with its causal factor and constant
extinction, "con-Spe; lin-Ext" = linear relationship between extinction with its causal factor
and constant speciation, "lin-Spe; lin-Ext" = linear relationship between speciation and
extinction with its causal factor. NP = number of parameters; logL = loglikelihood; AICc =
sample-size corrected Akaike Information Criterion; Lambda = speciation rate; Alpha = the
regression coefficient between speciation and time; Mu = extinction rate; Beta = the
regression coefficient between extinction and time. The best model is in bold.
Models NP logL AICc Lambda Alpha Mu Beta
con-Spe 1 -3060.35 6122.70 0.076 - - -
con-Spe; con-Ext 2 -3060.35 6124.71 0.076 - 0 -
exp-Spe 2 -3038.04 6080.09 0.058 0.019 - -
exp-Spe; con-Ext 3 -3038.04 6082.1 0.058 0.019 0 -
187
con-Spe; exp-Ext 3 -3060.35 6126.73 0.076 - 0 0.004
exp-Spe; exp-Ext 4 -3037.88 6083.81 0.057 0.024 0.003 0.062
lin-Spe 2 -3037.03 6078.08 0.053 0.002 - -
lin-Spe; con-Ext 3 -3037.03 6080.1 0.053 0.002 0 -
con-Spe; lin-Ext 3 -3060.45 6126.93 0.076 - 0 0
lin-Spe; lin-Ext 4 -3035.38 6078.82 0.041 0.007 0.032 -0.005
Table 9. Eight environmental-dependent diversification models representing the Climate
change hypothesis based on "Shi's phylogeny". The models were: "exp-Spe" = exponential
relationship between speciation with its causal factor, " exp-Spe; con-Ext" =exponential
relationship between speciation with its causal factor and constant extinction, "con-Spe;
exp-Ext" = exponential relationship between extinction with its causal factor and constant
speciation, "exp-Spe; exp-Ext" = exponential relationship between speciation and
extinction with its causal factor, "lin-Spe" = linear relationship between speciation with its
causal factor, "lin-Spe; con-Ext" = linear relationship between speciation with its causal
factor and constant extinction, "con-Spe; lin-Ext" = linear relationship between extinction
with its causal factor and constant speciation, "lin-Spe; lin-Ext" = linear relationship
between speciation and extinction with its causal factor. NP = number of parameters; logL
= loglikelihood; AICc = sample-size corrected Akaike Information Criterion; Lambda =
speciation rate; Alpha = the regression coefficient between speciation and temperature;
Mu = extinction rate; Beta = the regression coefficient between extinction and
temperature. The best model is in bold.
Models NP logL AICc Lambda Alpha Mu Beta
exp-Spe 2 -3036.89 6077.79 0.042 0.091 - -
exp-Spe; con-Ext 3 -3036.89 6079.81 0.042 0.09 0 -
con-Spe; exp-Ext 3 -3060.45 6126.93 0.076 - 0 0.005
exp-Spe; exp-Ext 4 -3036.89 6081.83 0.042 0.09 0 -0.005
lin-Spe 2 -3036.09 6076.2 0.031 0.007 - -
188
lin-Spe; con-Ext 3 -3036.09 6078.22 0.031 0.007 0 -
con-Spe; lin-Ext 3 -3060.45 6126.93 0.076 - 0 0
lin-Spe; lin-Ext 4 -3035.3 6078.65 0.033 0.008 0.054 -0.006
Table 10. Eight environmental-dependent diversification models representing the Sea
level hypothesis based on "Shi's phylogeny". The models were: "exp-Spe" = exponential
relationship between speciation with its causal factor, " exp-Spe; con-Ext" =exponential
relationship between speciation with its causal factor and constant extinction, "con-Spe;
exp-Ext" = exponential relationship between extinction with its causal factor and constant
speciation, "exp-Spe; exp-Ext" = exponential relationship between speciation and
extinction with its causal factor, "lin-Spe" = linear relationship between speciation with its
causal factor, "lin-Spe; con-Ext" = linear relationship between speciation with its causal
factor and constant extinction, "con-Spe; lin-Ext" = linear relationship between extinction
with its causal factor and constant speciation, "lin-Spe; lin-Ext" = linear relationship
between speciation and extinction with its causal factor. NP = number of parameters; logL
= loglikelihood; AICc = sample-size corrected Akaike Information Criterion; Lambda =
speciation rate; Alpha = the regression coefficient between speciation and sea level; Mu =
extinction rate; Beta = the regression coefficient between extinction and sea level. The
best model is in bold.
Models NP logL AICc Lambda Alpha Mu Beta
exp-Spe 2 -3044.06 6092.13 0.078 0.007 - -
exp-Spe; con-Ext 3 -3044.06 6094.15 0.078 0.007 0 -
con-Spe; exp-Ext 3 -3060.45 6126.93 0.076 - 0 0.005
exp-Spe; exp-Ext 4 -3044.06 6096.17 0.078 0.007 0 0.003
lin-Spe 2 -3043.05 6090.12 0.08 0 - -
lin-Spe; con-Ext 3 -3043.05 6092.13 0.08 0 0 -
con-Spe; lin-Ext 3 -3060.45 6126.93 0.076 - 0 0
lin-Spe; lin-Ext 4 -3043.05 6094.15 0.08 0 0 0
189
Table 11. Eight environmental-dependent diversification models representing the Andean
uplift hypothesis based on "Shi's phylogeny". The models were: "exp-Spe" = exponential
relationship between speciation with its causal factor, " exp-Spe; con-Ext" =exponential
relationship between speciation with its causal factor and constant extinction, "con-Spe;
exp-Ext" = exponential relationship between extinction with its causal factor and constant
speciation, "exp-Spe; exp-Ext" = exponential relationship between speciation and
extinction with its causal factor, "lin-Spe" = linear relationship between speciation with its
causal factor, "lin-Spe; con-Ext" = linear relationship between speciation with its causal
factor and constant extinction, "con-Spe; lin-Ext" = linear relationship between extinction
with its causal factor and constant speciation, "lin-Spe; lin-Ext" = linear relationship
between speciation and extinction with its causal factor. NP = number of parameters; logL
= loglikelihood; AICc = sample-size corrected Akaike Information Criterion; Lambda =
speciation rate; Alpha = the regression coefficient between speciation and andean uplift;
Mu = extinction rate; Beta = the regression coefficient between extinction and andean
uplift. The best model is in bold.
Models NP logL AICc Lambda Alpha Mu Beta
exp-Spe 2 -3038.6 6081.22 0.123 0 - -
exp-Spe; con-Ext 3 -3038.6 6083.23 0.123 0 0 -
con-Spe; exp-Ext 3 -3060.45 6126.93 0.076 - 0.077 -0.096
exp-Spe; exp-Ext 4 -3038.56 6085.18 0.133 0 0.018 -0
lin-Spe 2 -3037.87 6079.75 0.118 0 - -
lin-Spe; con-Ext 3 -3037.87 6081.76 0.118 0 0 -
con-Spe; lin-Ext 3 -3060.45 6126.93 0.076 - 0 0
lin-Spe; lin-Ext 4 -3037.6 6083.25 0.132 0 0.02 0
Table 12. Four diversity-dependent diversification models representing the Niche
availability hypothesis based on "Shi's phylogeny". The models were: "exp-Spe; con-Ext" =
190
exponential relationship between speciation with its causal factor and constant extinction,
"lin-Spe" = linear relationship between speciation with its causal factor, "lin-Spe; con-Ext"
= linear relationship between speciation with its causal factor and constant extinction,
"lin-Spe; lin-Ext" = linear relationship between speciation and extinction with its causal
factor. NP = number of parameters; logL = loglikelihood; AICc = sample-size corrected
Akaike Information Criterion; Lambda = speciation rate; Mu = extinction rate; k = carrying
capacity. The best model is in bold.
Model NP logL AICc Lambda Mu K
exp-Spe; con-Ext 3 -3232.78 6469.57 0.174 - 1300
lin-Spe 2 -3065.76 6137.56 0.276 0.092 1335.37
lin-Spe; con-Ext 3 -2377.78 4761.58 0.413 0.333 7958.54
lin-Spe; lin-Ext 4 -3049.34 6106.73 0.208 0.059 1300